TSTP Solution File: GEO223+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GEO223+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Sat Jul 16 02:52:59 EDT 2022
% Result : Theorem 103.67s 104.03s
% Output : Refutation 103.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO223+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : bliksem %s
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % DateTime : Sat Jun 18 11:55:28 EDT 2022
% 0.12/0.34 % CPUTime :
% 103.67/104.03 *** allocated 10000 integers for termspace/termends
% 103.67/104.03 *** allocated 10000 integers for clauses
% 103.67/104.03 *** allocated 10000 integers for justifications
% 103.67/104.03 Bliksem 1.12
% 103.67/104.03
% 103.67/104.03
% 103.67/104.03 Automatic Strategy Selection
% 103.67/104.03
% 103.67/104.03
% 103.67/104.03 Clauses:
% 103.67/104.03
% 103.67/104.03 { ! distinct_points( X, X ) }.
% 103.67/104.03 { ! distinct_lines( X, X ) }.
% 103.67/104.03 { ! convergent_lines( X, X ) }.
% 103.67/104.03 { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 103.67/104.03 ) }.
% 103.67/104.03 { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 103.67/104.03 }.
% 103.67/104.03 { ! convergent_lines( X, Y ), convergent_lines( X, Z ), convergent_lines( Y
% 103.67/104.03 , Z ) }.
% 103.67/104.03 { ! distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X
% 103.67/104.03 , Y ) ) }.
% 103.67/104.03 { ! distinct_points( X, Y ), ! apart_point_and_line( Y, line_connecting( X
% 103.67/104.03 , Y ) ) }.
% 103.67/104.03 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 103.67/104.03 , Y ), X ) }.
% 103.67/104.03 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 103.67/104.03 , Y ), Y ) }.
% 103.67/104.03 { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), apart_point_and_line
% 103.67/104.03 ( X, Z ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ),
% 103.67/104.03 apart_point_and_line( Y, T ) }.
% 103.67/104.03 { ! apart_point_and_line( X, Y ), distinct_points( X, Z ),
% 103.67/104.03 apart_point_and_line( Z, Y ) }.
% 103.67/104.03 { ! apart_point_and_line( X, Y ), distinct_lines( Y, Z ),
% 103.67/104.03 apart_point_and_line( X, Z ) }.
% 103.67/104.03 { ! convergent_lines( X, Y ), distinct_lines( Y, Z ), convergent_lines( X,
% 103.67/104.03 Z ) }.
% 103.67/104.03 { ! convergent_lines( parallel_through_point( Y, X ), Y ) }.
% 103.67/104.03 { ! apart_point_and_line( X, parallel_through_point( Y, X ) ) }.
% 103.67/104.03 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 103.67/104.03 apart_point_and_line( Z, Y ), convergent_lines( X, Y ) }.
% 103.67/104.03 { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 103.67/104.03 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 103.67/104.03 , convergent_lines( Y, Z ) }.
% 103.67/104.03 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 103.67/104.03 , unorthogonal_lines( Y, Z ) }.
% 103.67/104.03 { ! alpha1( X, Y ), convergent_lines( X, Y ) }.
% 103.67/104.03 { ! alpha1( X, Y ), unorthogonal_lines( X, Y ) }.
% 103.67/104.03 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Y )
% 103.67/104.03 }.
% 103.67/104.03 { ! unorthogonal_lines( orthogonal_through_point( Y, X ), Y ) }.
% 103.67/104.03 { ! apart_point_and_line( X, orthogonal_through_point( Y, X ) ) }.
% 103.67/104.03 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 103.67/104.03 apart_point_and_line( Z, Y ), unorthogonal_lines( X, T ),
% 103.67/104.03 unorthogonal_lines( Y, T ) }.
% 103.67/104.03 { distinct_lines( parallel_through_point( skol2, skol1 ),
% 103.67/104.03 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 103.67/104.03 ) ) }.
% 103.67/104.03
% 103.67/104.03 percentage equality = 0.000000, percentage horn = 0.555556
% 103.67/104.03 This a non-horn, non-equality problem
% 103.67/104.03
% 103.67/104.03
% 103.67/104.03 Options Used:
% 103.67/104.03
% 103.67/104.03 useres = 1
% 103.67/104.03 useparamod = 0
% 103.67/104.03 useeqrefl = 0
% 103.67/104.03 useeqfact = 0
% 103.67/104.03 usefactor = 1
% 103.67/104.03 usesimpsplitting = 0
% 103.67/104.03 usesimpdemod = 0
% 103.67/104.03 usesimpres = 3
% 103.67/104.03
% 103.67/104.03 resimpinuse = 1000
% 103.67/104.03 resimpclauses = 20000
% 103.67/104.03 substype = standard
% 103.67/104.03 backwardsubs = 1
% 103.67/104.03 selectoldest = 5
% 103.67/104.03
% 103.67/104.03 litorderings [0] = split
% 103.67/104.03 litorderings [1] = liftord
% 103.67/104.03
% 103.67/104.03 termordering = none
% 103.67/104.03
% 103.67/104.03 litapriori = 1
% 103.67/104.03 termapriori = 0
% 103.67/104.03 litaposteriori = 0
% 103.67/104.03 termaposteriori = 0
% 103.67/104.03 demodaposteriori = 0
% 103.67/104.03 ordereqreflfact = 0
% 103.67/104.03
% 103.67/104.03 litselect = none
% 103.67/104.03
% 103.67/104.03 maxweight = 15
% 103.67/104.03 maxdepth = 30000
% 103.67/104.03 maxlength = 115
% 103.67/104.03 maxnrvars = 195
% 103.67/104.03 excuselevel = 1
% 103.67/104.03 increasemaxweight = 1
% 103.67/104.03
% 103.67/104.03 maxselected = 10000000
% 103.67/104.03 maxnrclauses = 10000000
% 103.67/104.03
% 103.67/104.03 showgenerated = 0
% 103.67/104.03 showkept = 0
% 103.67/104.03 showselected = 0
% 103.67/104.03 showdeleted = 0
% 103.67/104.03 showresimp = 1
% 103.67/104.03 showstatus = 2000
% 103.67/104.03
% 103.67/104.03 prologoutput = 0
% 103.67/104.03 nrgoals = 5000000
% 103.67/104.03 totalproof = 1
% 103.67/104.03
% 103.67/104.03 Symbols occurring in the translation:
% 103.67/104.03
% 103.67/104.03 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 103.67/104.03 . [1, 2] (w:1, o:22, a:1, s:1, b:0),
% 103.67/104.03 ! [4, 1] (w:0, o:17, a:1, s:1, b:0),
% 103.67/104.03 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 103.67/104.03 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 103.67/104.03 distinct_points [36, 2] (w:1, o:47, a:1, s:1, b:0),
% 103.67/104.03 distinct_lines [37, 2] (w:1, o:48, a:1, s:1, b:0),
% 103.67/104.03 convergent_lines [38, 2] (w:1, o:46, a:1, s:1, b:0),
% 103.67/104.03 line_connecting [41, 2] (w:1, o:49, a:1, s:1, b:0),
% 103.67/104.03 apart_point_and_line [42, 2] (w:1, o:50, a:1, s:1, b:0),
% 103.67/104.03 intersection_point [43, 2] (w:1, o:51, a:1, s:1, b:0),
% 103.67/104.03 parallel_through_point [46, 2] (w:1, o:53, a:1, s:1, b:0),
% 103.67/104.03 unorthogonal_lines [49, 2] (w:1, o:54, a:1, s:1, b:0),
% 103.67/104.03 orthogonal_through_point [52, 2] (w:1, o:52, a:1, s:1, b:0),
% 103.67/104.03 alpha1 [53, 2] (w:1, o:55, a:1, s:1, b:0),
% 103.67/104.03 skol1 [54, 0] (w:1, o:15, a:1, s:1, b:0),
% 103.67/104.03 skol2 [55, 0] (w:1, o:16, a:1, s:1, b:0).
% 103.67/104.03
% 103.67/104.03
% 103.67/104.03 Starting Search:
% 103.67/104.03
% 103.67/104.03 *** allocated 15000 integers for clauses
% 103.67/104.03 *** allocated 22500 integers for clauses
% 103.67/104.03 *** allocated 33750 integers for clauses
% 103.67/104.03 *** allocated 15000 integers for termspace/termends
% 103.67/104.03 *** allocated 50625 integers for clauses
% 103.67/104.03 Resimplifying inuse:
% 103.67/104.03 Done
% 103.67/104.03
% 103.67/104.03 *** allocated 22500 integers for termspace/termends
% 103.67/104.03 *** allocated 75937 integers for clauses
% 103.67/104.03 *** allocated 33750 integers for termspace/termends
% 103.67/104.03 *** allocated 113905 integers for clauses
% 103.67/104.03 Resimplifying inuse:
% 103.67/104.03 Done
% 103.67/104.03
% 103.67/104.03 Failed to find proof!
% 103.67/104.03 maxweight = 15
% 103.67/104.03 maxnrclauses = 10000000
% 103.67/104.03 Generated: 1582279
% 103.67/104.03 Kept: 1986
% 103.67/104.03
% 103.67/104.03
% 103.67/104.03 The strategy used was not complete!
% 103.67/104.03
% 103.67/104.03 Increased maxweight to 16
% 103.67/104.03
% 103.67/104.03 Starting Search:
% 103.67/104.03
% 103.67/104.03 Resimplifying inuse:
% 103.67/104.03 Done
% 103.67/104.03
% 103.67/104.03
% 103.67/104.03 Intermediate Status:
% 103.67/104.03 Generated: 16769
% 103.67/104.03 Kept: 2007
% 103.67/104.03 Inuse: 208
% 103.67/104.03 Deleted: 0
% 103.67/104.03 Deletedinuse: 0
% 103.67/104.03
% 103.67/104.03 Resimplifying inuse:
% 103.67/104.03 Done
% 103.67/104.03
% 103.67/104.03 *** allocated 50625 integers for termspace/termends
% 103.67/104.03 *** allocated 170857 integers for clauses
% 103.67/104.03 Resimplifying inuse:
% 103.67/104.03 Done
% 103.67/104.03
% 103.67/104.03 *** allocated 75937 integers for termspace/termends
% 103.67/104.03 Resimplifying inuse:
% 103.67/104.03 Done
% 103.67/104.03
% 103.67/104.03 Failed to find proof!
% 103.67/104.03 maxweight = 16
% 103.67/104.03 maxnrclauses = 10000000
% 103.67/104.03 Generated: 4894792
% 103.67/104.03 Kept: 3528
% 103.67/104.03
% 103.67/104.03
% 103.67/104.03 The strategy used was not complete!
% 103.67/104.03
% 103.67/104.03 Increased maxweight to 17
% 103.67/104.03
% 103.67/104.03 Starting Search:
% 103.67/104.03
% 103.67/104.03 Resimplifying inuse:
% 103.67/104.03 Done
% 103.67/104.03
% 103.67/104.03
% 103.67/104.03 Intermediate Status:
% 103.67/104.03 Generated: 16268
% 103.67/104.03 Kept: 2006
% 103.67/104.03 Inuse: 192
% 103.67/104.03 Deleted: 0
% 103.67/104.03 Deletedinuse: 0
% 103.67/104.03
% 103.67/104.03 Resimplifying inuse:
% 103.67/104.03 Done
% 103.67/104.03
% 103.67/104.03 Resimplifying inuse:
% 103.67/104.03 Done
% 103.67/104.03
% 103.67/104.03
% 103.67/104.03 Intermediate Status:
% 103.67/104.03 Generated: 40363
% 103.67/104.03 Kept: 4033
% 103.67/104.03 Inuse: 351
% 103.67/104.03 Deleted: 1
% 103.67/104.03 Deletedinuse: 0
% 103.67/104.03
% 103.67/104.03 Resimplifying inuse:
% 103.67/104.03 Done
% 103.67/104.03
% 103.67/104.03 *** allocated 256285 integers for clauses
% 103.67/104.03 *** allocated 113905 integers for termspace/termends
% 103.67/104.03 Resimplifying inuse:
% 103.67/104.03 Done
% 103.67/104.03
% 103.67/104.03
% 103.67/104.03 Intermediate Status:
% 103.67/104.03 Generated: 3816415
% 103.67/104.03 Kept: 6034
% 103.67/104.03 Inuse: 2666
% 103.67/104.03 Deleted: 111
% 103.67/104.03 Deletedinuse: 9
% 103.67/104.03
% 103.67/104.03 Resimplifying inuse:
% 103.67/104.03 Done
% 103.67/104.03
% 103.67/104.03 *** allocated 384427 integers for clauses
% 103.67/104.03 *** allocated 170857 integers for termspace/termends
% 103.67/104.03 Resimplifying inuse:
% 103.67/104.03 Done
% 103.67/104.03
% 103.67/104.03
% 103.67/104.03 Intermediate Status:
% 103.67/104.03 Generated: 15165183
% 103.67/104.03 Kept: 8131
% 103.67/104.03 Inuse: 6842
% 103.67/104.03 Deleted: 360
% 103.67/104.03 Deletedinuse: 27
% 103.67/104.03
% 103.67/104.03 Resimplifying inuse:
% 103.67/104.03 Done
% 103.67/104.03
% 103.67/104.03 *** allocated 576640 integers for clauses
% 103.67/104.03 Resimplifying inuse:
% 103.67/104.03 Done
% 103.67/104.03
% 103.67/104.03
% 103.67/104.03 Intermediate Status:
% 103.67/104.03 Generated: 15349128
% 103.67/104.03 Kept: 10274
% 103.67/104.03 Inuse: 6889
% 103.67/104.03 Deleted: 362
% 103.67/104.03 Deletedinuse: 28
% 103.67/104.03
% 103.67/104.03 *** allocated 256285 integers for termspace/termends
% 103.67/104.03 Resimplifying inuse:
% 103.67/104.03 Done
% 103.67/104.03
% 103.67/104.03 Resimplifying inuse:
% 103.67/104.03 Done
% 103.67/104.03
% 103.67/104.03
% 103.67/104.03 Bliksems!, er is een bewijs:
% 103.67/104.03 % SZS status Theorem
% 103.67/104.03 % SZS output start Refutation
% 103.67/104.03
% 103.67/104.03 (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 103.67/104.03 (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 103.67/104.03 (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), distinct_lines( Y, Z )
% 103.67/104.03 , ! distinct_lines( X, Y ) }.
% 103.67/104.03 (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), convergent_lines( Y,
% 103.67/104.03 Z ), ! convergent_lines( X, Y ) }.
% 103.67/104.03 (8) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), !
% 103.67/104.03 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 103.67/104.03 (9) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), !
% 103.67/104.03 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 103.67/104.03 (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), apart_point_and_line(
% 103.67/104.03 X, Z ), ! apart_point_and_line( X, Y ) }.
% 103.67/104.03 (13) {G0,W9,D2,L3,V3,M1} I { ! convergent_lines( X, Y ), convergent_lines(
% 103.67/104.03 X, Z ), distinct_lines( Y, Z ) }.
% 103.67/104.03 (14) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines( parallel_through_point( Y
% 103.67/104.03 , X ), Y ) }.
% 103.67/104.03 (15) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 103.67/104.03 parallel_through_point( Y, X ) ) }.
% 103.67/104.03 (16) {G0,W12,D2,L4,V3,M2} I { ! distinct_lines( X, Y ), convergent_lines( X
% 103.67/104.03 , Y ), apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ) }.
% 103.67/104.03 (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), unorthogonal_lines(
% 103.67/104.03 X, Y ) }.
% 103.67/104.03 (18) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), !
% 103.67/104.03 unorthogonal_lines( X, Y ), convergent_lines( Y, Z ), alpha1( X, Z ) }.
% 103.67/104.03 (19) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), !
% 103.67/104.03 unorthogonal_lines( X, Y ), unorthogonal_lines( Y, Z ), alpha1( X, Z )
% 103.67/104.03 }.
% 103.67/104.03 (20) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! alpha1( X, Y ) }.
% 103.67/104.03 (21) {G0,W6,D2,L2,V2,M1} I { unorthogonal_lines( X, Y ), ! alpha1( X, Y )
% 103.67/104.03 }.
% 103.67/104.03 (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines( orthogonal_through_point
% 103.67/104.03 ( Y, X ), Y ) }.
% 103.67/104.03 (24) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 103.67/104.03 orthogonal_through_point( Y, X ) ) }.
% 103.67/104.03 (25) {G0,W15,D2,L5,V4,M2} I { ! distinct_lines( X, Y ),
% 103.67/104.03 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 103.67/104.03 unorthogonal_lines( Y, T ), unorthogonal_lines( X, T ) }.
% 103.67/104.03 (26) {G0,W9,D4,L1,V0,M1} I { distinct_lines( parallel_through_point( skol2
% 103.67/104.03 , skol1 ), orthogonal_through_point( orthogonal_through_point( skol2,
% 103.67/104.03 skol1 ), skol1 ) ) }.
% 103.67/104.03 (34) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), distinct_lines
% 103.67/104.03 ( X, Y ) }.
% 103.67/104.03 (35) {G2,W9,D2,L3,V3,M3} R(34,4) { distinct_lines( Z, X ), ! distinct_lines
% 103.67/104.03 ( Y, Z ), distinct_lines( X, Y ) }.
% 103.67/104.03 (37) {G1,W5,D3,L1,V2,M1} R(17,23) { convergent_lines(
% 103.67/104.03 orthogonal_through_point( X, Y ), X ) }.
% 103.67/104.03 (40) {G2,W8,D3,L2,V3,M2} R(5,37) { convergent_lines( X, Z ),
% 103.67/104.03 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 103.67/104.03 (41) {G1,W8,D3,L2,V3,M2} R(5,14) { ! convergent_lines(
% 103.67/104.03 parallel_through_point( Y, Z ), X ), convergent_lines( X, Y ) }.
% 103.67/104.03 (43) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 103.67/104.03 convergent_lines( X, Y ) }.
% 103.67/104.03 (44) {G2,W9,D2,L3,V3,M3} R(43,5) { convergent_lines( Z, X ), !
% 103.67/104.03 convergent_lines( Y, Z ), convergent_lines( X, Y ) }.
% 103.67/104.03 (46) {G2,W5,D3,L1,V2,M1} R(43,37) { convergent_lines( X,
% 103.67/104.03 orthogonal_through_point( X, Y ) ) }.
% 103.67/104.03 (91) {G3,W8,D3,L2,V3,M2} R(40,43) { convergent_lines( Z, X ),
% 103.67/104.03 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 103.67/104.03 (125) {G2,W11,D3,L3,V4,M3} R(41,5) { convergent_lines( Z, X ), !
% 103.67/104.03 convergent_lines( Z, parallel_through_point( Y, T ) ), convergent_lines(
% 103.67/104.03 X, Y ) }.
% 103.67/104.03 (192) {G3,W9,D2,L3,V3,M3} R(44,43) { convergent_lines( Z, X ),
% 103.67/104.03 convergent_lines( Z, Y ), ! convergent_lines( X, Y ) }.
% 103.67/104.03 (200) {G1,W12,D2,L4,V4,M2} R(12,12) { distinct_lines( X, Y ),
% 103.67/104.03 distinct_lines( Y, T ), apart_point_and_line( Z, T ), !
% 103.67/104.03 apart_point_and_line( Z, X ) }.
% 103.67/104.03 (209) {G1,W11,D3,L3,V3,M1} R(12,8) { distinct_lines( X, Y ), !
% 103.67/104.03 convergent_lines( Y, Z ), ! apart_point_and_line( intersection_point( Y,
% 103.67/104.03 Z ), X ) }.
% 103.67/104.03 (213) {G1,W8,D3,L2,V3,M1} R(12,24) { distinct_lines( X,
% 103.67/104.03 orthogonal_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 103.67/104.03 (215) {G2,W11,D3,L3,V4,M1} R(213,12) { distinct_lines( X,
% 103.67/104.03 orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ), !
% 103.67/104.03 apart_point_and_line( Z, T ) }.
% 103.67/104.03 (217) {G3,W9,D2,L3,V3,M3} R(35,34) { distinct_lines( Z, X ), distinct_lines
% 103.67/104.03 ( Z, Y ), ! distinct_lines( X, Y ) }.
% 103.67/104.03 (222) {G2,W9,D2,L3,V3,M1} R(13,34) { ! convergent_lines( X, Y ),
% 103.67/104.03 convergent_lines( X, Z ), distinct_lines( Z, Y ) }.
% 103.67/104.03 (245) {G1,W14,D3,L4,V3,M1} R(16,9) { convergent_lines( X, Y ), !
% 103.67/104.03 distinct_lines( X, Y ), ! convergent_lines( Z, X ), apart_point_and_line
% 103.67/104.03 ( intersection_point( Z, X ), Y ) }.
% 103.67/104.03 (254) {G1,W13,D3,L3,V3,M1} R(16,15) { convergent_lines( X,
% 103.67/104.03 parallel_through_point( Y, Z ) ), ! distinct_lines( X,
% 103.67/104.03 parallel_through_point( Y, Z ) ), apart_point_and_line( Z, X ) }.
% 103.67/104.03 (274) {G1,W12,D2,L4,V3,M2} R(18,21) { ! convergent_lines( X, Y ),
% 103.67/104.03 convergent_lines( Y, Z ), unorthogonal_lines( X, Z ), !
% 103.67/104.03 unorthogonal_lines( X, Y ) }.
% 103.67/104.03 (289) {G1,W12,D2,L4,V3,M2} R(19,20) { ! convergent_lines( X, Y ),
% 103.67/104.03 convergent_lines( X, Z ), ! unorthogonal_lines( X, Y ),
% 103.67/104.03 unorthogonal_lines( Y, Z ) }.
% 103.67/104.03 (300) {G2,W9,D4,L1,V0,M1} R(26,34) { distinct_lines(
% 103.67/104.03 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 103.67/104.03 ), parallel_through_point( skol2, skol1 ) ) }.
% 103.67/104.03 (302) {G1,W16,D3,L4,V4,M1} R(25,23) { ! distinct_lines( X,
% 103.67/104.03 orthogonal_through_point( Y, Z ) ), apart_point_and_line( T, X ),
% 103.67/104.03 apart_point_and_line( T, orthogonal_through_point( Y, Z ) ),
% 103.67/104.03 unorthogonal_lines( X, Y ) }.
% 103.67/104.03 (303) {G1,W16,D3,L4,V4,M1} R(25,23) { ! distinct_lines(
% 103.67/104.03 orthogonal_through_point( X, Y ), Z ), apart_point_and_line( T,
% 103.67/104.03 orthogonal_through_point( X, Y ) ), apart_point_and_line( T, Z ),
% 103.67/104.03 unorthogonal_lines( Z, X ) }.
% 103.67/104.03 (1213) {G3,W14,D3,L4,V5,M1} R(215,12) { distinct_lines( X,
% 103.67/104.03 orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ),
% 103.67/104.03 distinct_lines( U, T ), ! apart_point_and_line( Z, U ) }.
% 103.67/104.03 (1215) {G4,W8,D3,L2,V3,M1} F(1213);r(34) { distinct_lines(
% 103.67/104.03 orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 103.67/104.03 (2328) {G2,W17,D3,L5,V5,M1} R(200,209) { distinct_lines( X, Y ),
% 103.67/104.03 distinct_lines( Y, Z ), distinct_lines( Z, T ), ! convergent_lines( T, U
% 103.67/104.03 ), ! apart_point_and_line( intersection_point( T, U ), X ) }.
% 103.67/104.03 (2354) {G3,W11,D3,L3,V3,M1} F(2328);r(34) { ! convergent_lines( Y, Z ),
% 103.67/104.03 distinct_lines( Y, X ), ! apart_point_and_line( intersection_point( Y, Z
% 103.67/104.03 ), X ) }.
% 103.67/104.03 (2961) {G4,W8,D3,L2,V3,M1} R(274,23);r(91) { convergent_lines( Z, X ), !
% 103.67/104.03 unorthogonal_lines( orthogonal_through_point( X, Y ), Z ) }.
% 103.67/104.03 (2965) {G5,W16,D3,L4,V4,M1} R(2961,289) { convergent_lines( X, Y ), !
% 103.67/104.03 convergent_lines( Z, orthogonal_through_point( Y, T ) ), convergent_lines
% 103.67/104.03 ( Z, X ), ! unorthogonal_lines( Z, orthogonal_through_point( Y, T ) ) }.
% 103.67/104.03 (2966) {G6,W10,D3,L2,V2,M1} F(2965);r(2) { ! convergent_lines( X,
% 103.67/104.03 orthogonal_through_point( X, Y ) ), ! unorthogonal_lines( X,
% 103.67/104.03 orthogonal_through_point( X, Y ) ) }.
% 103.67/104.03 (2967) {G7,W5,D3,L1,V2,M1} S(2966);r(46) { ! unorthogonal_lines( X,
% 103.67/104.03 orthogonal_through_point( X, Y ) ) }.
% 103.67/104.03 (4368) {G4,W12,D2,L4,V3,M2} R(245,2354);f { convergent_lines( X, Y ), !
% 103.67/104.03 convergent_lines( Z, X ), distinct_lines( Z, Y ), ! distinct_lines( X, Y
% 103.67/104.03 ) }.
% 103.67/104.03 (4384) {G5,W12,D2,L4,V3,M2} R(4368,34) { convergent_lines( X, Y ), !
% 103.67/104.03 convergent_lines( Z, X ), ! distinct_lines( Y, X ), distinct_lines( Z, Y
% 103.67/104.03 ) }.
% 103.67/104.03 (4393) {G6,W12,D2,L4,V3,M2} R(4384,34) { convergent_lines( X, Y ), !
% 103.67/104.03 convergent_lines( Z, X ), distinct_lines( Y, Z ), ! distinct_lines( Y, X
% 103.67/104.03 ) }.
% 103.67/104.03 (4397) {G7,W15,D2,L5,V4,M3} R(4393,217) { convergent_lines( X, Y ), !
% 103.67/104.03 convergent_lines( Z, X ), distinct_lines( Y, T ), ! distinct_lines( X, T
% 103.67/104.03 ), distinct_lines( Y, Z ) }.
% 103.67/104.03 (4404) {G8,W12,D2,L4,V3,M2} F(4397) { convergent_lines( X, Y ), !
% 103.67/104.03 convergent_lines( Z, X ), ! distinct_lines( X, Z ), distinct_lines( Y, Z
% 103.67/104.03 ) }.
% 103.67/104.03 (4411) {G9,W15,D2,L5,V4,M1} R(4404,222) { convergent_lines( X, Y ), !
% 103.67/104.03 convergent_lines( Z, X ), ! convergent_lines( T, Z ), convergent_lines( T
% 103.67/104.03 , X ), distinct_lines( Y, Z ) }.
% 103.67/104.03 (4420) {G10,W9,D2,L3,V2,M1} F(4411);r(2) { ! convergent_lines( Y, X ), !
% 103.67/104.03 convergent_lines( X, Y ), distinct_lines( X, Y ) }.
% 103.67/104.03 (4441) {G11,W6,D2,L2,V2,M1} S(4420);r(43) { ! convergent_lines( X, Y ),
% 103.67/104.03 distinct_lines( X, Y ) }.
% 103.67/104.03 (4540) {G2,W14,D3,L2,V3,M1} R(254,24) { convergent_lines(
% 103.67/104.03 orthogonal_through_point( X, Y ), parallel_through_point( Z, Y ) ), !
% 103.67/104.03 distinct_lines( orthogonal_through_point( X, Y ), parallel_through_point
% 103.67/104.03 ( Z, Y ) ) }.
% 103.67/104.03 (4549) {G2,W17,D3,L3,V4,M2} R(302,23) { ! distinct_lines(
% 103.67/104.03 orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ),
% 103.67/104.03 apart_point_and_line( T, orthogonal_through_point( X, Z ) ),
% 103.67/104.03 apart_point_and_line( T, orthogonal_through_point( X, Y ) ) }.
% 103.67/104.03 (4550) {G8,W17,D4,L3,V4,M2} R(303,2967) { ! distinct_lines(
% 103.67/104.03 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ),
% 103.67/104.03 apart_point_and_line( T, X ), apart_point_and_line( T,
% 103.67/104.03 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ) ) }.
% 103.67/104.03 (4959) {G3,W9,D4,L1,V0,M1} R(4540,300) { convergent_lines(
% 103.67/104.03 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 103.67/104.03 ), parallel_through_point( skol2, skol1 ) ) }.
% 103.67/104.03 (5045) {G4,W10,D4,L2,V1,M2} R(4959,125) { convergent_lines( X, skol2 ),
% 103.67/104.03 convergent_lines( orthogonal_through_point( orthogonal_through_point(
% 103.67/104.03 skol2, skol1 ), skol1 ), X ) }.
% 103.67/104.03 (6163) {G3,W12,D3,L2,V3,M1} R(4549,24) { ! distinct_lines(
% 103.67/104.03 orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ),
% 103.67/104.03 apart_point_and_line( Y, orthogonal_through_point( X, Z ) ) }.
% 103.67/104.03 (6393) {G5,W14,D3,L2,V4,M2} R(6163,1215) { distinct_lines(
% 103.67/104.03 orthogonal_through_point( T, Y ), orthogonal_through_point( X, Z ) ), !
% 103.67/104.03 distinct_lines( orthogonal_through_point( X, Y ),
% 103.67/104.03 orthogonal_through_point( X, Z ) ) }.
% 103.67/104.03 (6399) {G4,W16,D5,L2,V3,M1} R(6163,8) { ! convergent_lines(
% 103.67/104.03 orthogonal_through_point( X, Y ), Z ), ! distinct_lines(
% 103.67/104.03 orthogonal_through_point( X, intersection_point( orthogonal_through_point
% 103.67/104.03 ( X, Y ), Z ) ), orthogonal_through_point( X, Y ) ) }.
% 103.67/104.03 (6503) {G12,W14,D3,L2,V4,M1} R(6393,4441) { ! convergent_lines(
% 103.67/104.03 orthogonal_through_point( Z, Y ), orthogonal_through_point( Z, T ) ),
% 103.67/104.03 distinct_lines( orthogonal_through_point( X, Y ),
% 103.67/104.03 orthogonal_through_point( Z, T ) ) }.
% 103.67/104.03 (6558) {G13,W14,D3,L2,V4,M1} R(6503,34) { ! convergent_lines(
% 103.67/104.03 orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ),
% 103.67/104.03 distinct_lines( orthogonal_through_point( X, Z ),
% 103.67/104.03 orthogonal_through_point( T, Y ) ) }.
% 103.67/104.03 (7216) {G14,W16,D5,L2,V3,M2} R(6399,6558) { ! convergent_lines(
% 103.67/104.03 orthogonal_through_point( X, Y ), orthogonal_through_point( X,
% 103.67/104.03 intersection_point( orthogonal_through_point( X, Y ), Z ) ) ), !
% 103.67/104.03 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 103.67/104.03 (7217) {G13,W16,D5,L2,V3,M2} R(6399,6503) { ! convergent_lines(
% 103.67/104.03 orthogonal_through_point( X, intersection_point( orthogonal_through_point
% 103.67/104.03 ( X, Y ), Z ) ), orthogonal_through_point( X, Y ) ), ! convergent_lines(
% 103.67/104.03 orthogonal_through_point( X, Y ), Z ) }.
% 103.67/104.03 (7238) {G15,W11,D5,L1,V2,M1} R(7216,37) { ! convergent_lines(
% 103.67/104.03 orthogonal_through_point( X, Y ), orthogonal_through_point( X,
% 103.67/104.03 intersection_point( orthogonal_through_point( X, Y ), X ) ) ) }.
% 103.67/104.03 (7269) {G16,W15,D6,L1,V0,M1} R(7238,5045) { convergent_lines(
% 103.67/104.03 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ),
% 103.67/104.03 intersection_point( orthogonal_through_point( orthogonal_through_point(
% 103.67/104.03 skol2, skol1 ), skol1 ), orthogonal_through_point( skol2, skol1 ) ) ),
% 103.67/104.03 skol2 ) }.
% 103.67/104.03 (7879) {G9,W10,D4,L2,V3,M1} R(4550,24) { ! distinct_lines(
% 103.67/104.03 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ),
% 103.67/104.03 apart_point_and_line( Z, X ) }.
% 103.67/104.03 (7931) {G10,W12,D4,L2,V4,M2} R(7879,1215) { distinct_lines(
% 103.67/104.03 orthogonal_through_point( T, Z ), X ), ! distinct_lines(
% 103.67/104.03 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ) }.
% 103.67/104.03 (7938) {G10,W12,D4,L2,V3,M1} R(7879,9) { ! convergent_lines( Z, X ), !
% 103.67/104.03 distinct_lines( orthogonal_through_point( orthogonal_through_point( X, Y
% 103.67/104.03 ), intersection_point( Z, X ) ), X ) }.
% 103.67/104.03 (9772) {G12,W12,D4,L2,V4,M1} R(7931,4441) { ! convergent_lines(
% 103.67/104.03 orthogonal_through_point( orthogonal_through_point( Z, T ), Y ), Z ),
% 103.67/104.03 distinct_lines( orthogonal_through_point( X, Y ), Z ) }.
% 103.67/104.03 (11439) {G13,W12,D4,L2,V3,M2} R(7938,9772) { ! convergent_lines(
% 103.67/104.03 orthogonal_through_point( orthogonal_through_point( Y, Z ),
% 103.67/104.03 intersection_point( X, Y ) ), Y ), ! convergent_lines( X, Y ) }.
% 103.67/104.03 (11787) {G14,W12,D4,L2,V3,M2} R(11439,43) { ! convergent_lines( X, Z ), !
% 103.67/104.03 convergent_lines( orthogonal_through_point( orthogonal_through_point( X,
% 103.67/104.03 Y ), intersection_point( Z, X ) ), X ) }.
% 103.67/104.03 (12018) {G15,W15,D4,L3,V4,M3} R(11787,192) { convergent_lines(
% 103.67/104.03 orthogonal_through_point( orthogonal_through_point( X, Z ),
% 103.67/104.03 intersection_point( Y, X ) ), T ), ! convergent_lines( X, T ), !
% 103.67/104.03 convergent_lines( X, Y ) }.
% 103.67/104.03 (12034) {G16,W12,D4,L2,V3,M2} F(12018) { ! convergent_lines( X, Z ),
% 103.67/104.03 convergent_lines( orthogonal_through_point( orthogonal_through_point( X,
% 103.67/104.03 Y ), intersection_point( Z, X ) ), Z ) }.
% 103.67/104.03 (12041) {G17,W7,D4,L1,V3,M1} R(12034,7217);r(43) { ! convergent_lines(
% 103.67/104.03 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ) }.
% 103.67/104.03 (12241) {G18,W0,D0,L0,V0,M0} R(12041,7269) { }.
% 103.67/104.03
% 103.67/104.03
% 103.67/104.03 % SZS output end Refutation
% 103.67/104.03 found a proof!
% 103.67/104.03
% 103.67/104.03
% 103.67/104.03 Unprocessed initial clauses:
% 103.67/104.03
% 103.67/104.03 (12243) {G0,W3,D2,L1,V1,M1} { ! distinct_points( X, X ) }.
% 103.67/104.03 (12244) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 103.67/104.03 (12245) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 103.67/104.03 (12246) {G0,W9,D2,L3,V3,M3} { ! distinct_points( X, Y ), distinct_points(
% 103.67/104.03 X, Z ), distinct_points( Y, Z ) }.
% 103.67/104.03 (12247) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ), distinct_lines( X
% 103.67/104.03 , Z ), distinct_lines( Y, Z ) }.
% 103.67/104.03 (12248) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), convergent_lines
% 103.67/104.03 ( X, Z ), convergent_lines( Y, Z ) }.
% 103.67/104.03 (12249) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 103.67/104.03 apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 103.67/104.03 (12250) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 103.67/104.03 apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 103.67/104.03 (12251) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 103.67/104.03 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 103.67/104.03 (12252) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 103.67/104.03 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 103.67/104.03 (12253) {G0,W18,D2,L6,V4,M6} { ! distinct_points( X, Y ), ! distinct_lines
% 103.67/104.03 ( Z, T ), apart_point_and_line( X, Z ), apart_point_and_line( X, T ),
% 103.67/104.03 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ) }.
% 103.67/104.03 (12254) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 103.67/104.03 distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 103.67/104.03 (12255) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 103.67/104.03 distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 103.67/104.03 (12256) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), distinct_lines(
% 103.67/104.03 Y, Z ), convergent_lines( X, Z ) }.
% 103.67/104.03 (12257) {G0,W5,D3,L1,V2,M1} { ! convergent_lines( parallel_through_point(
% 103.67/104.03 Y, X ), Y ) }.
% 103.67/104.03 (12258) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 103.67/104.03 parallel_through_point( Y, X ) ) }.
% 103.67/104.03 (12259) {G0,W12,D2,L4,V3,M4} { ! distinct_lines( X, Y ),
% 103.67/104.03 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 103.67/104.03 convergent_lines( X, Y ) }.
% 103.67/104.03 (12260) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), unorthogonal_lines
% 103.67/104.03 ( X, Y ) }.
% 103.67/104.03 (12261) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 103.67/104.03 unorthogonal_lines( X, Y ), alpha1( X, Z ), convergent_lines( Y, Z ) }.
% 103.67/104.03 (12262) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 103.67/104.03 unorthogonal_lines( X, Y ), alpha1( X, Z ), unorthogonal_lines( Y, Z )
% 103.67/104.03 }.
% 103.67/104.03 (12263) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), convergent_lines( X, Y )
% 103.67/104.03 }.
% 103.67/104.03 (12264) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), unorthogonal_lines( X, Y )
% 103.67/104.03 }.
% 103.67/104.03 (12265) {G0,W9,D2,L3,V2,M3} { ! convergent_lines( X, Y ), !
% 103.67/104.03 unorthogonal_lines( X, Y ), alpha1( X, Y ) }.
% 103.67/104.03 (12266) {G0,W5,D3,L1,V2,M1} { ! unorthogonal_lines(
% 103.67/104.03 orthogonal_through_point( Y, X ), Y ) }.
% 103.67/104.03 (12267) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 103.67/104.03 orthogonal_through_point( Y, X ) ) }.
% 103.67/104.03 (12268) {G0,W15,D2,L5,V4,M5} { ! distinct_lines( X, Y ),
% 103.67/104.03 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 103.67/104.03 unorthogonal_lines( X, T ), unorthogonal_lines( Y, T ) }.
% 103.67/104.03 (12269) {G0,W9,D4,L1,V0,M1} { distinct_lines( parallel_through_point(
% 103.67/104.03 skol2, skol1 ), orthogonal_through_point( orthogonal_through_point( skol2
% 103.67/104.03 , skol1 ), skol1 ) ) }.
% 103.67/104.03
% 103.67/104.03
% 103.67/104.03 Total Proof:
% 103.67/104.03
% 103.67/104.03 subsumption: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 103.67/104.03 parent0: (12244) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 0
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 103.67/104.03 parent0: (12245) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 0
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 103.67/104.03 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 103.67/104.03 parent0: (12247) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ),
% 103.67/104.03 distinct_lines( X, Z ), distinct_lines( Y, Z ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 Z := Z
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 2
% 103.67/104.03 1 ==> 0
% 103.67/104.03 2 ==> 1
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 103.67/104.03 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 103.67/104.03 parent0: (12248) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ),
% 103.67/104.03 convergent_lines( X, Z ), convergent_lines( Y, Z ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 Z := Z
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 2
% 103.67/104.03 1 ==> 0
% 103.67/104.03 2 ==> 1
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (8) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), !
% 103.67/104.03 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 103.67/104.03 parent0: (12251) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 103.67/104.03 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 0
% 103.67/104.03 1 ==> 1
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (9) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), !
% 103.67/104.03 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 103.67/104.03 parent0: (12252) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 103.67/104.03 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 0
% 103.67/104.03 1 ==> 1
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 103.67/104.03 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 103.67/104.03 parent0: (12255) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 103.67/104.03 distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 Z := Z
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 2
% 103.67/104.03 1 ==> 0
% 103.67/104.03 2 ==> 1
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (13) {G0,W9,D2,L3,V3,M1} I { ! convergent_lines( X, Y ),
% 103.67/104.03 convergent_lines( X, Z ), distinct_lines( Y, Z ) }.
% 103.67/104.03 parent0: (12256) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ),
% 103.67/104.03 distinct_lines( Y, Z ), convergent_lines( X, Z ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 Z := Z
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 0
% 103.67/104.03 1 ==> 2
% 103.67/104.03 2 ==> 1
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (14) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines(
% 103.67/104.03 parallel_through_point( Y, X ), Y ) }.
% 103.67/104.03 parent0: (12257) {G0,W5,D3,L1,V2,M1} { ! convergent_lines(
% 103.67/104.03 parallel_through_point( Y, X ), Y ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 0
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (15) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 103.67/104.03 parallel_through_point( Y, X ) ) }.
% 103.67/104.03 parent0: (12258) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 103.67/104.03 parallel_through_point( Y, X ) ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 0
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (16) {G0,W12,D2,L4,V3,M2} I { ! distinct_lines( X, Y ),
% 103.67/104.03 convergent_lines( X, Y ), apart_point_and_line( Z, X ),
% 103.67/104.03 apart_point_and_line( Z, Y ) }.
% 103.67/104.03 parent0: (12259) {G0,W12,D2,L4,V3,M4} { ! distinct_lines( X, Y ),
% 103.67/104.03 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 103.67/104.03 convergent_lines( X, Y ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 Z := Z
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 0
% 103.67/104.03 1 ==> 2
% 103.67/104.03 2 ==> 3
% 103.67/104.03 3 ==> 1
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ),
% 103.67/104.03 unorthogonal_lines( X, Y ) }.
% 103.67/104.03 parent0: (12260) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ),
% 103.67/104.03 unorthogonal_lines( X, Y ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 0
% 103.67/104.03 1 ==> 1
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (18) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), !
% 103.67/104.03 unorthogonal_lines( X, Y ), convergent_lines( Y, Z ), alpha1( X, Z ) }.
% 103.67/104.03 parent0: (12261) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 103.67/104.03 unorthogonal_lines( X, Y ), alpha1( X, Z ), convergent_lines( Y, Z ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 Z := Z
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 0
% 103.67/104.03 1 ==> 1
% 103.67/104.03 2 ==> 3
% 103.67/104.03 3 ==> 2
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (19) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), !
% 103.67/104.03 unorthogonal_lines( X, Y ), unorthogonal_lines( Y, Z ), alpha1( X, Z )
% 103.67/104.03 }.
% 103.67/104.03 parent0: (12262) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 103.67/104.03 unorthogonal_lines( X, Y ), alpha1( X, Z ), unorthogonal_lines( Y, Z )
% 103.67/104.03 }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 Z := Z
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 0
% 103.67/104.03 1 ==> 1
% 103.67/104.03 2 ==> 3
% 103.67/104.03 3 ==> 2
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (20) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), !
% 103.67/104.03 alpha1( X, Y ) }.
% 103.67/104.03 parent0: (12263) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), convergent_lines
% 103.67/104.03 ( X, Y ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 1
% 103.67/104.03 1 ==> 0
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (21) {G0,W6,D2,L2,V2,M1} I { unorthogonal_lines( X, Y ), !
% 103.67/104.03 alpha1( X, Y ) }.
% 103.67/104.03 parent0: (12264) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ),
% 103.67/104.03 unorthogonal_lines( X, Y ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 1
% 103.67/104.03 1 ==> 0
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 103.67/104.03 orthogonal_through_point( Y, X ), Y ) }.
% 103.67/104.03 parent0: (12266) {G0,W5,D3,L1,V2,M1} { ! unorthogonal_lines(
% 103.67/104.03 orthogonal_through_point( Y, X ), Y ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 0
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (24) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 103.67/104.03 orthogonal_through_point( Y, X ) ) }.
% 103.67/104.03 parent0: (12267) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 103.67/104.03 orthogonal_through_point( Y, X ) ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 0
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (25) {G0,W15,D2,L5,V4,M2} I { ! distinct_lines( X, Y ),
% 103.67/104.03 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 103.67/104.03 unorthogonal_lines( Y, T ), unorthogonal_lines( X, T ) }.
% 103.67/104.03 parent0: (12268) {G0,W15,D2,L5,V4,M5} { ! distinct_lines( X, Y ),
% 103.67/104.03 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 103.67/104.03 unorthogonal_lines( X, T ), unorthogonal_lines( Y, T ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 Z := Z
% 103.67/104.03 T := T
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 0
% 103.67/104.03 1 ==> 1
% 103.67/104.03 2 ==> 2
% 103.67/104.03 3 ==> 4
% 103.67/104.03 4 ==> 3
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (26) {G0,W9,D4,L1,V0,M1} I { distinct_lines(
% 103.67/104.03 parallel_through_point( skol2, skol1 ), orthogonal_through_point(
% 103.67/104.03 orthogonal_through_point( skol2, skol1 ), skol1 ) ) }.
% 103.67/104.03 parent0: (12269) {G0,W9,D4,L1,V0,M1} { distinct_lines(
% 103.67/104.03 parallel_through_point( skol2, skol1 ), orthogonal_through_point(
% 103.67/104.03 orthogonal_through_point( skol2, skol1 ), skol1 ) ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 0
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 resolution: (12421) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 103.67/104.03 distinct_lines( X, Y ) }.
% 103.67/104.03 parent0[0]: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 103.67/104.03 parent1[0]: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 103.67/104.03 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 end
% 103.67/104.03 substitution1:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 Z := X
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (34) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 103.67/104.03 distinct_lines( X, Y ) }.
% 103.67/104.03 parent0: (12421) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 103.67/104.03 distinct_lines( X, Y ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := Y
% 103.67/104.03 Y := X
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 1
% 103.67/104.03 1 ==> 0
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 resolution: (12423) {G1,W9,D2,L3,V3,M3} { distinct_lines( Y, X ),
% 103.67/104.03 distinct_lines( Z, Y ), ! distinct_lines( X, Z ) }.
% 103.67/104.03 parent0[0]: (34) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 103.67/104.03 distinct_lines( X, Y ) }.
% 103.67/104.03 parent1[0]: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 103.67/104.03 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := Y
% 103.67/104.03 Y := X
% 103.67/104.03 end
% 103.67/104.03 substitution1:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Z
% 103.67/104.03 Z := Y
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (35) {G2,W9,D2,L3,V3,M3} R(34,4) { distinct_lines( Z, X ), !
% 103.67/104.03 distinct_lines( Y, Z ), distinct_lines( X, Y ) }.
% 103.67/104.03 parent0: (12423) {G1,W9,D2,L3,V3,M3} { distinct_lines( Y, X ),
% 103.67/104.03 distinct_lines( Z, Y ), ! distinct_lines( X, Z ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := Y
% 103.67/104.03 Y := X
% 103.67/104.03 Z := Z
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 2
% 103.67/104.03 1 ==> 0
% 103.67/104.03 2 ==> 1
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 resolution: (12426) {G1,W5,D3,L1,V2,M1} { convergent_lines(
% 103.67/104.03 orthogonal_through_point( X, Y ), X ) }.
% 103.67/104.03 parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 103.67/104.03 orthogonal_through_point( Y, X ), Y ) }.
% 103.67/104.03 parent1[1]: (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ),
% 103.67/104.03 unorthogonal_lines( X, Y ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := Y
% 103.67/104.03 Y := X
% 103.67/104.03 end
% 103.67/104.03 substitution1:
% 103.67/104.03 X := orthogonal_through_point( X, Y )
% 103.67/104.03 Y := X
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (37) {G1,W5,D3,L1,V2,M1} R(17,23) { convergent_lines(
% 103.67/104.03 orthogonal_through_point( X, Y ), X ) }.
% 103.67/104.03 parent0: (12426) {G1,W5,D3,L1,V2,M1} { convergent_lines(
% 103.67/104.03 orthogonal_through_point( X, Y ), X ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 0
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 resolution: (12427) {G1,W8,D3,L2,V3,M2} { convergent_lines(
% 103.67/104.03 orthogonal_through_point( X, Y ), Z ), convergent_lines( X, Z ) }.
% 103.67/104.03 parent0[2]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 103.67/104.03 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 103.67/104.03 parent1[0]: (37) {G1,W5,D3,L1,V2,M1} R(17,23) { convergent_lines(
% 103.67/104.03 orthogonal_through_point( X, Y ), X ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := orthogonal_through_point( X, Y )
% 103.67/104.03 Y := X
% 103.67/104.03 Z := Z
% 103.67/104.03 end
% 103.67/104.03 substitution1:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (40) {G2,W8,D3,L2,V3,M2} R(5,37) { convergent_lines( X, Z ),
% 103.67/104.03 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 103.67/104.03 parent0: (12427) {G1,W8,D3,L2,V3,M2} { convergent_lines(
% 103.67/104.03 orthogonal_through_point( X, Y ), Z ), convergent_lines( X, Z ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 Z := Z
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 1
% 103.67/104.03 1 ==> 0
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 resolution: (12428) {G1,W8,D3,L2,V3,M2} { convergent_lines( Z, X ), !
% 103.67/104.03 convergent_lines( parallel_through_point( X, Y ), Z ) }.
% 103.67/104.03 parent0[0]: (14) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines(
% 103.67/104.03 parallel_through_point( Y, X ), Y ) }.
% 103.67/104.03 parent1[0]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 103.67/104.03 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := Y
% 103.67/104.03 Y := X
% 103.67/104.03 end
% 103.67/104.03 substitution1:
% 103.67/104.03 X := parallel_through_point( X, Y )
% 103.67/104.03 Y := Z
% 103.67/104.03 Z := X
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (41) {G1,W8,D3,L2,V3,M2} R(5,14) { ! convergent_lines(
% 103.67/104.03 parallel_through_point( Y, Z ), X ), convergent_lines( X, Y ) }.
% 103.67/104.03 parent0: (12428) {G1,W8,D3,L2,V3,M2} { convergent_lines( Z, X ), !
% 103.67/104.03 convergent_lines( parallel_through_point( X, Y ), Z ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := Y
% 103.67/104.03 Y := Z
% 103.67/104.03 Z := X
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 1
% 103.67/104.03 1 ==> 0
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 resolution: (12430) {G1,W6,D2,L2,V2,M2} { convergent_lines( Y, X ), !
% 103.67/104.03 convergent_lines( X, Y ) }.
% 103.67/104.03 parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 103.67/104.03 parent1[0]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 103.67/104.03 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 end
% 103.67/104.03 substitution1:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 Z := X
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (43) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 103.67/104.03 convergent_lines( X, Y ) }.
% 103.67/104.03 parent0: (12430) {G1,W6,D2,L2,V2,M2} { convergent_lines( Y, X ), !
% 103.67/104.03 convergent_lines( X, Y ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := Y
% 103.67/104.03 Y := X
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 1
% 103.67/104.03 1 ==> 0
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 resolution: (12432) {G1,W9,D2,L3,V3,M3} { convergent_lines( Y, X ),
% 103.67/104.03 convergent_lines( Z, Y ), ! convergent_lines( X, Z ) }.
% 103.67/104.03 parent0[0]: (43) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 103.67/104.03 convergent_lines( X, Y ) }.
% 103.67/104.03 parent1[0]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 103.67/104.03 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := Y
% 103.67/104.03 Y := X
% 103.67/104.03 end
% 103.67/104.03 substitution1:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Z
% 103.67/104.03 Z := Y
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (44) {G2,W9,D2,L3,V3,M3} R(43,5) { convergent_lines( Z, X ), !
% 103.67/104.03 convergent_lines( Y, Z ), convergent_lines( X, Y ) }.
% 103.67/104.03 parent0: (12432) {G1,W9,D2,L3,V3,M3} { convergent_lines( Y, X ),
% 103.67/104.03 convergent_lines( Z, Y ), ! convergent_lines( X, Z ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := Y
% 103.67/104.03 Y := X
% 103.67/104.03 Z := Z
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 2
% 103.67/104.03 1 ==> 0
% 103.67/104.03 2 ==> 1
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 resolution: (12435) {G2,W5,D3,L1,V2,M1} { convergent_lines( X,
% 103.67/104.03 orthogonal_through_point( X, Y ) ) }.
% 103.67/104.03 parent0[0]: (43) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 103.67/104.03 convergent_lines( X, Y ) }.
% 103.67/104.03 parent1[0]: (37) {G1,W5,D3,L1,V2,M1} R(17,23) { convergent_lines(
% 103.67/104.03 orthogonal_through_point( X, Y ), X ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := orthogonal_through_point( X, Y )
% 103.67/104.03 end
% 103.67/104.03 substitution1:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (46) {G2,W5,D3,L1,V2,M1} R(43,37) { convergent_lines( X,
% 103.67/104.03 orthogonal_through_point( X, Y ) ) }.
% 103.67/104.03 parent0: (12435) {G2,W5,D3,L1,V2,M1} { convergent_lines( X,
% 103.67/104.03 orthogonal_through_point( X, Y ) ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 0
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 resolution: (12436) {G2,W8,D3,L2,V3,M2} { convergent_lines( Y, X ),
% 103.67/104.03 convergent_lines( orthogonal_through_point( X, Z ), Y ) }.
% 103.67/104.03 parent0[0]: (43) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 103.67/104.03 convergent_lines( X, Y ) }.
% 103.67/104.03 parent1[0]: (40) {G2,W8,D3,L2,V3,M2} R(5,37) { convergent_lines( X, Z ),
% 103.67/104.03 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := Y
% 103.67/104.03 Y := X
% 103.67/104.03 end
% 103.67/104.03 substitution1:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Z
% 103.67/104.03 Z := Y
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (91) {G3,W8,D3,L2,V3,M2} R(40,43) { convergent_lines( Z, X ),
% 103.67/104.03 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 103.67/104.03 parent0: (12436) {G2,W8,D3,L2,V3,M2} { convergent_lines( Y, X ),
% 103.67/104.03 convergent_lines( orthogonal_through_point( X, Z ), Y ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Z
% 103.67/104.03 Z := Y
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 0
% 103.67/104.03 1 ==> 1
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 resolution: (12439) {G1,W11,D3,L3,V4,M3} { convergent_lines( Z, X ),
% 103.67/104.03 convergent_lines( T, Z ), ! convergent_lines( T, parallel_through_point(
% 103.67/104.03 X, Y ) ) }.
% 103.67/104.03 parent0[0]: (41) {G1,W8,D3,L2,V3,M2} R(5,14) { ! convergent_lines(
% 103.67/104.03 parallel_through_point( Y, Z ), X ), convergent_lines( X, Y ) }.
% 103.67/104.03 parent1[1]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 103.67/104.03 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := Z
% 103.67/104.03 Y := X
% 103.67/104.03 Z := Y
% 103.67/104.03 end
% 103.67/104.03 substitution1:
% 103.67/104.03 X := T
% 103.67/104.03 Y := parallel_through_point( X, Y )
% 103.67/104.03 Z := Z
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (125) {G2,W11,D3,L3,V4,M3} R(41,5) { convergent_lines( Z, X )
% 103.67/104.03 , ! convergent_lines( Z, parallel_through_point( Y, T ) ),
% 103.67/104.03 convergent_lines( X, Y ) }.
% 103.67/104.03 parent0: (12439) {G1,W11,D3,L3,V4,M3} { convergent_lines( Z, X ),
% 103.67/104.03 convergent_lines( T, Z ), ! convergent_lines( T, parallel_through_point(
% 103.67/104.03 X, Y ) ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := Y
% 103.67/104.03 Y := T
% 103.67/104.03 Z := X
% 103.67/104.03 T := Z
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 2
% 103.67/104.03 1 ==> 0
% 103.67/104.03 2 ==> 1
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 resolution: (12444) {G2,W9,D2,L3,V3,M3} { convergent_lines( Y, X ), !
% 103.67/104.03 convergent_lines( Z, X ), convergent_lines( Y, Z ) }.
% 103.67/104.03 parent0[0]: (43) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 103.67/104.03 convergent_lines( X, Y ) }.
% 103.67/104.03 parent1[0]: (44) {G2,W9,D2,L3,V3,M3} R(43,5) { convergent_lines( Z, X ), !
% 103.67/104.03 convergent_lines( Y, Z ), convergent_lines( X, Y ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := Y
% 103.67/104.03 Y := X
% 103.67/104.03 end
% 103.67/104.03 substitution1:
% 103.67/104.03 X := Y
% 103.67/104.03 Y := Z
% 103.67/104.03 Z := X
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (192) {G3,W9,D2,L3,V3,M3} R(44,43) { convergent_lines( Z, X )
% 103.67/104.03 , convergent_lines( Z, Y ), ! convergent_lines( X, Y ) }.
% 103.67/104.03 parent0: (12444) {G2,W9,D2,L3,V3,M3} { convergent_lines( Y, X ), !
% 103.67/104.03 convergent_lines( Z, X ), convergent_lines( Y, Z ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := Y
% 103.67/104.03 Y := Z
% 103.67/104.03 Z := X
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 1
% 103.67/104.03 1 ==> 2
% 103.67/104.03 2 ==> 0
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 resolution: (12448) {G1,W12,D2,L4,V4,M4} { distinct_lines( X, Y ),
% 103.67/104.03 apart_point_and_line( Z, Y ), distinct_lines( T, X ), !
% 103.67/104.03 apart_point_and_line( Z, T ) }.
% 103.67/104.03 parent0[2]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 103.67/104.03 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 103.67/104.03 parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 103.67/104.03 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := Z
% 103.67/104.03 Y := X
% 103.67/104.03 Z := Y
% 103.67/104.03 end
% 103.67/104.03 substitution1:
% 103.67/104.03 X := Z
% 103.67/104.03 Y := T
% 103.67/104.03 Z := X
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (200) {G1,W12,D2,L4,V4,M2} R(12,12) { distinct_lines( X, Y ),
% 103.67/104.03 distinct_lines( Y, T ), apart_point_and_line( Z, T ), !
% 103.67/104.03 apart_point_and_line( Z, X ) }.
% 103.67/104.03 parent0: (12448) {G1,W12,D2,L4,V4,M4} { distinct_lines( X, Y ),
% 103.67/104.03 apart_point_and_line( Z, Y ), distinct_lines( T, X ), !
% 103.67/104.03 apart_point_and_line( Z, T ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := Y
% 103.67/104.03 Y := T
% 103.67/104.03 Z := Z
% 103.67/104.03 T := X
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 1
% 103.67/104.03 1 ==> 2
% 103.67/104.03 2 ==> 0
% 103.67/104.03 3 ==> 3
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 resolution: (12450) {G1,W11,D3,L3,V3,M3} { ! convergent_lines( X, Y ),
% 103.67/104.03 distinct_lines( Z, X ), ! apart_point_and_line( intersection_point( X, Y
% 103.67/104.03 ), Z ) }.
% 103.67/104.03 parent0[1]: (8) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), !
% 103.67/104.03 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 103.67/104.03 parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 103.67/104.03 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 end
% 103.67/104.03 substitution1:
% 103.67/104.03 X := intersection_point( X, Y )
% 103.67/104.03 Y := Z
% 103.67/104.03 Z := X
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (209) {G1,W11,D3,L3,V3,M1} R(12,8) { distinct_lines( X, Y ), !
% 103.67/104.03 convergent_lines( Y, Z ), ! apart_point_and_line( intersection_point( Y
% 103.67/104.03 , Z ), X ) }.
% 103.67/104.03 parent0: (12450) {G1,W11,D3,L3,V3,M3} { ! convergent_lines( X, Y ),
% 103.67/104.03 distinct_lines( Z, X ), ! apart_point_and_line( intersection_point( X, Y
% 103.67/104.03 ), Z ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := Y
% 103.67/104.03 Y := Z
% 103.67/104.03 Z := X
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 1
% 103.67/104.03 1 ==> 0
% 103.67/104.03 2 ==> 2
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 resolution: (12451) {G1,W8,D3,L2,V3,M2} { distinct_lines( Z,
% 103.67/104.03 orthogonal_through_point( Y, X ) ), ! apart_point_and_line( X, Z ) }.
% 103.67/104.03 parent0[0]: (24) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 103.67/104.03 orthogonal_through_point( Y, X ) ) }.
% 103.67/104.03 parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 103.67/104.03 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 end
% 103.67/104.03 substitution1:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Z
% 103.67/104.03 Z := orthogonal_through_point( Y, X )
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (213) {G1,W8,D3,L2,V3,M1} R(12,24) { distinct_lines( X,
% 103.67/104.03 orthogonal_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 103.67/104.03 parent0: (12451) {G1,W8,D3,L2,V3,M2} { distinct_lines( Z,
% 103.67/104.03 orthogonal_through_point( Y, X ) ), ! apart_point_and_line( X, Z ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := Z
% 103.67/104.03 Y := Y
% 103.67/104.03 Z := X
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 0
% 103.67/104.03 1 ==> 1
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 resolution: (12452) {G1,W11,D3,L3,V4,M3} { distinct_lines( X,
% 103.67/104.03 orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ), !
% 103.67/104.03 apart_point_and_line( Z, T ) }.
% 103.67/104.03 parent0[1]: (213) {G1,W8,D3,L2,V3,M1} R(12,24) { distinct_lines( X,
% 103.67/104.03 orthogonal_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 103.67/104.03 parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 103.67/104.03 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 Z := Z
% 103.67/104.03 end
% 103.67/104.03 substitution1:
% 103.67/104.03 X := Z
% 103.67/104.03 Y := T
% 103.67/104.03 Z := X
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (215) {G2,W11,D3,L3,V4,M1} R(213,12) { distinct_lines( X,
% 103.67/104.03 orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ), !
% 103.67/104.03 apart_point_and_line( Z, T ) }.
% 103.67/104.03 parent0: (12452) {G1,W11,D3,L3,V4,M3} { distinct_lines( X,
% 103.67/104.03 orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ), !
% 103.67/104.03 apart_point_and_line( Z, T ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 Z := Z
% 103.67/104.03 T := T
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 0
% 103.67/104.03 1 ==> 1
% 103.67/104.03 2 ==> 2
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 resolution: (12456) {G2,W9,D2,L3,V3,M3} { distinct_lines( Y, X ), !
% 103.67/104.03 distinct_lines( Z, X ), distinct_lines( Y, Z ) }.
% 103.67/104.03 parent0[0]: (34) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 103.67/104.03 distinct_lines( X, Y ) }.
% 103.67/104.03 parent1[0]: (35) {G2,W9,D2,L3,V3,M3} R(34,4) { distinct_lines( Z, X ), !
% 103.67/104.03 distinct_lines( Y, Z ), distinct_lines( X, Y ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := Y
% 103.67/104.03 Y := X
% 103.67/104.03 end
% 103.67/104.03 substitution1:
% 103.67/104.03 X := Y
% 103.67/104.03 Y := Z
% 103.67/104.03 Z := X
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (217) {G3,W9,D2,L3,V3,M3} R(35,34) { distinct_lines( Z, X ),
% 103.67/104.03 distinct_lines( Z, Y ), ! distinct_lines( X, Y ) }.
% 103.67/104.03 parent0: (12456) {G2,W9,D2,L3,V3,M3} { distinct_lines( Y, X ), !
% 103.67/104.03 distinct_lines( Z, X ), distinct_lines( Y, Z ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := Y
% 103.67/104.03 Y := Z
% 103.67/104.03 Z := X
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 1
% 103.67/104.03 1 ==> 2
% 103.67/104.03 2 ==> 0
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 resolution: (12460) {G1,W9,D2,L3,V3,M3} { distinct_lines( Y, X ), !
% 103.67/104.03 convergent_lines( Z, X ), convergent_lines( Z, Y ) }.
% 103.67/104.03 parent0[0]: (34) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 103.67/104.03 distinct_lines( X, Y ) }.
% 103.67/104.03 parent1[2]: (13) {G0,W9,D2,L3,V3,M1} I { ! convergent_lines( X, Y ),
% 103.67/104.03 convergent_lines( X, Z ), distinct_lines( Y, Z ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := Y
% 103.67/104.03 Y := X
% 103.67/104.03 end
% 103.67/104.03 substitution1:
% 103.67/104.03 X := Z
% 103.67/104.03 Y := X
% 103.67/104.03 Z := Y
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (222) {G2,W9,D2,L3,V3,M1} R(13,34) { ! convergent_lines( X, Y
% 103.67/104.03 ), convergent_lines( X, Z ), distinct_lines( Z, Y ) }.
% 103.67/104.03 parent0: (12460) {G1,W9,D2,L3,V3,M3} { distinct_lines( Y, X ), !
% 103.67/104.03 convergent_lines( Z, X ), convergent_lines( Z, Y ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := Y
% 103.67/104.03 Y := Z
% 103.67/104.03 Z := X
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 2
% 103.67/104.03 1 ==> 0
% 103.67/104.03 2 ==> 1
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 resolution: (12462) {G1,W14,D3,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 103.67/104.03 distinct_lines( Y, Z ), convergent_lines( Y, Z ), apart_point_and_line(
% 103.67/104.03 intersection_point( X, Y ), Z ) }.
% 103.67/104.03 parent0[1]: (9) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), !
% 103.67/104.03 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 103.67/104.03 parent1[2]: (16) {G0,W12,D2,L4,V3,M2} I { ! distinct_lines( X, Y ),
% 103.67/104.03 convergent_lines( X, Y ), apart_point_and_line( Z, X ),
% 103.67/104.03 apart_point_and_line( Z, Y ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 end
% 103.67/104.03 substitution1:
% 103.67/104.03 X := Y
% 103.67/104.03 Y := Z
% 103.67/104.03 Z := intersection_point( X, Y )
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (245) {G1,W14,D3,L4,V3,M1} R(16,9) { convergent_lines( X, Y )
% 103.67/104.03 , ! distinct_lines( X, Y ), ! convergent_lines( Z, X ),
% 103.67/104.03 apart_point_and_line( intersection_point( Z, X ), Y ) }.
% 103.67/104.03 parent0: (12462) {G1,W14,D3,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 103.67/104.03 distinct_lines( Y, Z ), convergent_lines( Y, Z ), apart_point_and_line(
% 103.67/104.03 intersection_point( X, Y ), Z ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := Z
% 103.67/104.03 Y := X
% 103.67/104.03 Z := Y
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 2
% 103.67/104.03 1 ==> 1
% 103.67/104.03 2 ==> 0
% 103.67/104.03 3 ==> 3
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 resolution: (12466) {G1,W13,D3,L3,V3,M3} { ! distinct_lines( Z,
% 103.67/104.03 parallel_through_point( Y, X ) ), convergent_lines( Z,
% 103.67/104.03 parallel_through_point( Y, X ) ), apart_point_and_line( X, Z ) }.
% 103.67/104.03 parent0[0]: (15) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 103.67/104.03 parallel_through_point( Y, X ) ) }.
% 103.67/104.03 parent1[3]: (16) {G0,W12,D2,L4,V3,M2} I { ! distinct_lines( X, Y ),
% 103.67/104.03 convergent_lines( X, Y ), apart_point_and_line( Z, X ),
% 103.67/104.03 apart_point_and_line( Z, Y ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 end
% 103.67/104.03 substitution1:
% 103.67/104.03 X := Z
% 103.67/104.03 Y := parallel_through_point( Y, X )
% 103.67/104.03 Z := X
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (254) {G1,W13,D3,L3,V3,M1} R(16,15) { convergent_lines( X,
% 103.67/104.03 parallel_through_point( Y, Z ) ), ! distinct_lines( X,
% 103.67/104.03 parallel_through_point( Y, Z ) ), apart_point_and_line( Z, X ) }.
% 103.67/104.03 parent0: (12466) {G1,W13,D3,L3,V3,M3} { ! distinct_lines( Z,
% 103.67/104.03 parallel_through_point( Y, X ) ), convergent_lines( Z,
% 103.67/104.03 parallel_through_point( Y, X ) ), apart_point_and_line( X, Z ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := Z
% 103.67/104.03 Y := Y
% 103.67/104.03 Z := X
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 1
% 103.67/104.03 1 ==> 0
% 103.67/104.03 2 ==> 2
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 resolution: (12468) {G1,W12,D2,L4,V3,M4} { unorthogonal_lines( X, Y ), !
% 103.67/104.03 convergent_lines( X, Z ), ! unorthogonal_lines( X, Z ), convergent_lines
% 103.67/104.03 ( Z, Y ) }.
% 103.67/104.03 parent0[1]: (21) {G0,W6,D2,L2,V2,M1} I { unorthogonal_lines( X, Y ), !
% 103.67/104.03 alpha1( X, Y ) }.
% 103.67/104.03 parent1[3]: (18) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), !
% 103.67/104.03 unorthogonal_lines( X, Y ), convergent_lines( Y, Z ), alpha1( X, Z ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 end
% 103.67/104.03 substitution1:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Z
% 103.67/104.03 Z := Y
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (274) {G1,W12,D2,L4,V3,M2} R(18,21) { ! convergent_lines( X, Y
% 103.67/104.03 ), convergent_lines( Y, Z ), unorthogonal_lines( X, Z ), !
% 103.67/104.03 unorthogonal_lines( X, Y ) }.
% 103.67/104.03 parent0: (12468) {G1,W12,D2,L4,V3,M4} { unorthogonal_lines( X, Y ), !
% 103.67/104.03 convergent_lines( X, Z ), ! unorthogonal_lines( X, Z ), convergent_lines
% 103.67/104.03 ( Z, Y ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Z
% 103.67/104.03 Z := Y
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 2
% 103.67/104.03 1 ==> 0
% 103.67/104.03 2 ==> 3
% 103.67/104.03 3 ==> 1
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 resolution: (12470) {G1,W12,D2,L4,V3,M4} { convergent_lines( X, Y ), !
% 103.67/104.03 convergent_lines( X, Z ), ! unorthogonal_lines( X, Z ),
% 103.67/104.03 unorthogonal_lines( Z, Y ) }.
% 103.67/104.03 parent0[1]: (20) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! alpha1
% 103.67/104.03 ( X, Y ) }.
% 103.67/104.03 parent1[3]: (19) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), !
% 103.67/104.03 unorthogonal_lines( X, Y ), unorthogonal_lines( Y, Z ), alpha1( X, Z )
% 103.67/104.03 }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 end
% 103.67/104.03 substitution1:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Z
% 103.67/104.03 Z := Y
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (289) {G1,W12,D2,L4,V3,M2} R(19,20) { ! convergent_lines( X, Y
% 103.67/104.03 ), convergent_lines( X, Z ), ! unorthogonal_lines( X, Y ),
% 103.67/104.03 unorthogonal_lines( Y, Z ) }.
% 103.67/104.03 parent0: (12470) {G1,W12,D2,L4,V3,M4} { convergent_lines( X, Y ), !
% 103.67/104.03 convergent_lines( X, Z ), ! unorthogonal_lines( X, Z ),
% 103.67/104.03 unorthogonal_lines( Z, Y ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Z
% 103.67/104.03 Z := Y
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 1
% 103.67/104.03 1 ==> 0
% 103.67/104.03 2 ==> 2
% 103.67/104.03 3 ==> 3
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 resolution: (12471) {G1,W9,D4,L1,V0,M1} { distinct_lines(
% 103.67/104.03 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 103.67/104.03 ), parallel_through_point( skol2, skol1 ) ) }.
% 103.67/104.03 parent0[0]: (34) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 103.67/104.03 distinct_lines( X, Y ) }.
% 103.67/104.03 parent1[0]: (26) {G0,W9,D4,L1,V0,M1} I { distinct_lines(
% 103.67/104.03 parallel_through_point( skol2, skol1 ), orthogonal_through_point(
% 103.67/104.03 orthogonal_through_point( skol2, skol1 ), skol1 ) ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := orthogonal_through_point( orthogonal_through_point( skol2, skol1 )
% 103.67/104.03 , skol1 )
% 103.67/104.03 Y := parallel_through_point( skol2, skol1 )
% 103.67/104.03 end
% 103.67/104.03 substitution1:
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (300) {G2,W9,D4,L1,V0,M1} R(26,34) { distinct_lines(
% 103.67/104.03 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 103.67/104.03 ), parallel_through_point( skol2, skol1 ) ) }.
% 103.67/104.03 parent0: (12471) {G1,W9,D4,L1,V0,M1} { distinct_lines(
% 103.67/104.03 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 103.67/104.03 ), parallel_through_point( skol2, skol1 ) ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 0
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 resolution: (12472) {G1,W16,D3,L4,V4,M4} { ! distinct_lines( Z,
% 103.67/104.03 orthogonal_through_point( X, Y ) ), apart_point_and_line( T, Z ),
% 103.67/104.03 apart_point_and_line( T, orthogonal_through_point( X, Y ) ),
% 103.67/104.03 unorthogonal_lines( Z, X ) }.
% 103.67/104.03 parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 103.67/104.03 orthogonal_through_point( Y, X ), Y ) }.
% 103.67/104.03 parent1[3]: (25) {G0,W15,D2,L5,V4,M2} I { ! distinct_lines( X, Y ),
% 103.67/104.03 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 103.67/104.03 unorthogonal_lines( Y, T ), unorthogonal_lines( X, T ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := Y
% 103.67/104.03 Y := X
% 103.67/104.03 end
% 103.67/104.03 substitution1:
% 103.67/104.03 X := Z
% 103.67/104.03 Y := orthogonal_through_point( X, Y )
% 103.67/104.03 Z := T
% 103.67/104.03 T := X
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (302) {G1,W16,D3,L4,V4,M1} R(25,23) { ! distinct_lines( X,
% 103.67/104.03 orthogonal_through_point( Y, Z ) ), apart_point_and_line( T, X ),
% 103.67/104.03 apart_point_and_line( T, orthogonal_through_point( Y, Z ) ),
% 103.67/104.03 unorthogonal_lines( X, Y ) }.
% 103.67/104.03 parent0: (12472) {G1,W16,D3,L4,V4,M4} { ! distinct_lines( Z,
% 103.67/104.03 orthogonal_through_point( X, Y ) ), apart_point_and_line( T, Z ),
% 103.67/104.03 apart_point_and_line( T, orthogonal_through_point( X, Y ) ),
% 103.67/104.03 unorthogonal_lines( Z, X ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := Y
% 103.67/104.03 Y := Z
% 103.67/104.03 Z := X
% 103.67/104.03 T := T
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 0
% 103.67/104.03 1 ==> 1
% 103.67/104.03 2 ==> 2
% 103.67/104.03 3 ==> 3
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 resolution: (12476) {G1,W16,D3,L4,V4,M4} { ! distinct_lines(
% 103.67/104.03 orthogonal_through_point( X, Y ), Z ), apart_point_and_line( T,
% 103.67/104.03 orthogonal_through_point( X, Y ) ), apart_point_and_line( T, Z ),
% 103.67/104.03 unorthogonal_lines( Z, X ) }.
% 103.67/104.03 parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 103.67/104.03 orthogonal_through_point( Y, X ), Y ) }.
% 103.67/104.03 parent1[4]: (25) {G0,W15,D2,L5,V4,M2} I { ! distinct_lines( X, Y ),
% 103.67/104.03 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 103.67/104.03 unorthogonal_lines( Y, T ), unorthogonal_lines( X, T ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := Y
% 103.67/104.03 Y := X
% 103.67/104.03 end
% 103.67/104.03 substitution1:
% 103.67/104.03 X := orthogonal_through_point( X, Y )
% 103.67/104.03 Y := Z
% 103.67/104.03 Z := T
% 103.67/104.03 T := X
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (303) {G1,W16,D3,L4,V4,M1} R(25,23) { ! distinct_lines(
% 103.67/104.03 orthogonal_through_point( X, Y ), Z ), apart_point_and_line( T,
% 103.67/104.03 orthogonal_through_point( X, Y ) ), apart_point_and_line( T, Z ),
% 103.67/104.03 unorthogonal_lines( Z, X ) }.
% 103.67/104.03 parent0: (12476) {G1,W16,D3,L4,V4,M4} { ! distinct_lines(
% 103.67/104.03 orthogonal_through_point( X, Y ), Z ), apart_point_and_line( T,
% 103.67/104.03 orthogonal_through_point( X, Y ) ), apart_point_and_line( T, Z ),
% 103.67/104.03 unorthogonal_lines( Z, X ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 Z := Z
% 103.67/104.03 T := T
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 0
% 103.67/104.03 1 ==> 1
% 103.67/104.03 2 ==> 2
% 103.67/104.03 3 ==> 3
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 resolution: (12478) {G1,W14,D3,L4,V5,M4} { distinct_lines( X,
% 103.67/104.03 orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ),
% 103.67/104.03 distinct_lines( U, T ), ! apart_point_and_line( Z, U ) }.
% 103.67/104.03 parent0[2]: (215) {G2,W11,D3,L3,V4,M1} R(213,12) { distinct_lines( X,
% 103.67/104.03 orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ), !
% 103.67/104.03 apart_point_and_line( Z, T ) }.
% 103.67/104.03 parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 103.67/104.03 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 Z := Z
% 103.67/104.03 T := T
% 103.67/104.03 end
% 103.67/104.03 substitution1:
% 103.67/104.03 X := Z
% 103.67/104.03 Y := U
% 103.67/104.03 Z := T
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (1213) {G3,W14,D3,L4,V5,M1} R(215,12) { distinct_lines( X,
% 103.67/104.03 orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ),
% 103.67/104.03 distinct_lines( U, T ), ! apart_point_and_line( Z, U ) }.
% 103.67/104.03 parent0: (12478) {G1,W14,D3,L4,V5,M4} { distinct_lines( X,
% 103.67/104.03 orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ),
% 103.67/104.03 distinct_lines( U, T ), ! apart_point_and_line( Z, U ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 Z := Z
% 103.67/104.03 T := T
% 103.67/104.03 U := U
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 0
% 103.67/104.03 1 ==> 1
% 103.67/104.03 2 ==> 2
% 103.67/104.03 3 ==> 3
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 factor: (12484) {G3,W13,D3,L3,V3,M3} { distinct_lines( X,
% 103.67/104.03 orthogonal_through_point( Y, Z ) ), distinct_lines(
% 103.67/104.03 orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 103.67/104.03 parent0[0, 2]: (1213) {G3,W14,D3,L4,V5,M1} R(215,12) { distinct_lines( X,
% 103.67/104.03 orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ),
% 103.67/104.03 distinct_lines( U, T ), ! apart_point_and_line( Z, U ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 Z := Z
% 103.67/104.03 T := orthogonal_through_point( Y, Z )
% 103.67/104.03 U := X
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 resolution: (12490) {G2,W13,D3,L3,V3,M3} { distinct_lines(
% 103.67/104.03 orthogonal_through_point( Y, Z ), X ), distinct_lines(
% 103.67/104.03 orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 103.67/104.03 parent0[0]: (34) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 103.67/104.03 distinct_lines( X, Y ) }.
% 103.67/104.03 parent1[0]: (12484) {G3,W13,D3,L3,V3,M3} { distinct_lines( X,
% 103.67/104.03 orthogonal_through_point( Y, Z ) ), distinct_lines(
% 103.67/104.03 orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := orthogonal_through_point( Y, Z )
% 103.67/104.03 Y := X
% 103.67/104.03 end
% 103.67/104.03 substitution1:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 Z := Z
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 factor: (12492) {G2,W8,D3,L2,V3,M2} { distinct_lines(
% 103.67/104.03 orthogonal_through_point( X, Y ), Z ), ! apart_point_and_line( Y, Z ) }.
% 103.67/104.03 parent0[0, 1]: (12490) {G2,W13,D3,L3,V3,M3} { distinct_lines(
% 103.67/104.03 orthogonal_through_point( Y, Z ), X ), distinct_lines(
% 103.67/104.03 orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := Z
% 103.67/104.03 Y := X
% 103.67/104.03 Z := Y
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (1215) {G4,W8,D3,L2,V3,M1} F(1213);r(34) { distinct_lines(
% 103.67/104.03 orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 103.67/104.03 parent0: (12492) {G2,W8,D3,L2,V3,M2} { distinct_lines(
% 103.67/104.03 orthogonal_through_point( X, Y ), Z ), ! apart_point_and_line( Y, Z ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := Y
% 103.67/104.03 Y := Z
% 103.67/104.03 Z := X
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 0
% 103.67/104.03 1 ==> 1
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 resolution: (12494) {G2,W17,D3,L5,V5,M5} { distinct_lines( X, Y ), !
% 103.67/104.03 convergent_lines( Y, Z ), distinct_lines( T, U ), distinct_lines( U, X )
% 103.67/104.03 , ! apart_point_and_line( intersection_point( Y, Z ), T ) }.
% 103.67/104.03 parent0[2]: (209) {G1,W11,D3,L3,V3,M1} R(12,8) { distinct_lines( X, Y ), !
% 103.67/104.03 convergent_lines( Y, Z ), ! apart_point_and_line( intersection_point( Y,
% 103.67/104.03 Z ), X ) }.
% 103.67/104.03 parent1[2]: (200) {G1,W12,D2,L4,V4,M2} R(12,12) { distinct_lines( X, Y ),
% 103.67/104.03 distinct_lines( Y, T ), apart_point_and_line( Z, T ), !
% 103.67/104.03 apart_point_and_line( Z, X ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 Z := Z
% 103.67/104.03 end
% 103.67/104.03 substitution1:
% 103.67/104.03 X := T
% 103.67/104.03 Y := U
% 103.67/104.03 Z := intersection_point( Y, Z )
% 103.67/104.03 T := X
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (2328) {G2,W17,D3,L5,V5,M1} R(200,209) { distinct_lines( X, Y
% 103.67/104.03 ), distinct_lines( Y, Z ), distinct_lines( Z, T ), ! convergent_lines( T
% 103.67/104.03 , U ), ! apart_point_and_line( intersection_point( T, U ), X ) }.
% 103.67/104.03 parent0: (12494) {G2,W17,D3,L5,V5,M5} { distinct_lines( X, Y ), !
% 103.67/104.03 convergent_lines( Y, Z ), distinct_lines( T, U ), distinct_lines( U, X )
% 103.67/104.03 , ! apart_point_and_line( intersection_point( Y, Z ), T ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := Z
% 103.67/104.03 Y := T
% 103.67/104.03 Z := U
% 103.67/104.03 T := X
% 103.67/104.03 U := Y
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 2
% 103.67/104.03 1 ==> 3
% 103.67/104.03 2 ==> 0
% 103.67/104.03 3 ==> 1
% 103.67/104.03 4 ==> 4
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 factor: (12500) {G2,W14,D3,L4,V3,M4} { distinct_lines( X, Y ),
% 103.67/104.03 distinct_lines( Y, X ), ! convergent_lines( Y, Z ), !
% 103.67/104.03 apart_point_and_line( intersection_point( Y, Z ), X ) }.
% 103.67/104.03 parent0[0, 2]: (2328) {G2,W17,D3,L5,V5,M1} R(200,209) { distinct_lines( X,
% 103.67/104.03 Y ), distinct_lines( Y, Z ), distinct_lines( Z, T ), ! convergent_lines(
% 103.67/104.03 T, U ), ! apart_point_and_line( intersection_point( T, U ), X ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 Z := X
% 103.67/104.03 T := Y
% 103.67/104.03 U := Z
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 resolution: (12506) {G2,W14,D3,L4,V3,M4} { distinct_lines( Y, X ),
% 103.67/104.03 distinct_lines( Y, X ), ! convergent_lines( Y, Z ), !
% 103.67/104.03 apart_point_and_line( intersection_point( Y, Z ), X ) }.
% 103.67/104.03 parent0[0]: (34) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 103.67/104.03 distinct_lines( X, Y ) }.
% 103.67/104.03 parent1[0]: (12500) {G2,W14,D3,L4,V3,M4} { distinct_lines( X, Y ),
% 103.67/104.03 distinct_lines( Y, X ), ! convergent_lines( Y, Z ), !
% 103.67/104.03 apart_point_and_line( intersection_point( Y, Z ), X ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := Y
% 103.67/104.03 Y := X
% 103.67/104.03 end
% 103.67/104.03 substitution1:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 Z := Z
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 factor: (12508) {G2,W11,D3,L3,V3,M3} { distinct_lines( X, Y ), !
% 103.67/104.03 convergent_lines( X, Z ), ! apart_point_and_line( intersection_point( X,
% 103.67/104.03 Z ), Y ) }.
% 103.67/104.03 parent0[0, 1]: (12506) {G2,W14,D3,L4,V3,M4} { distinct_lines( Y, X ),
% 103.67/104.03 distinct_lines( Y, X ), ! convergent_lines( Y, Z ), !
% 103.67/104.03 apart_point_and_line( intersection_point( Y, Z ), X ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := Y
% 103.67/104.03 Y := X
% 103.67/104.03 Z := Z
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (2354) {G3,W11,D3,L3,V3,M1} F(2328);r(34) { ! convergent_lines
% 103.67/104.03 ( Y, Z ), distinct_lines( Y, X ), ! apart_point_and_line(
% 103.67/104.03 intersection_point( Y, Z ), X ) }.
% 103.67/104.03 parent0: (12508) {G2,W11,D3,L3,V3,M3} { distinct_lines( X, Y ), !
% 103.67/104.03 convergent_lines( X, Z ), ! apart_point_and_line( intersection_point( X,
% 103.67/104.03 Z ), Y ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := Y
% 103.67/104.03 Y := X
% 103.67/104.03 Z := Z
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 1
% 103.67/104.03 1 ==> 0
% 103.67/104.03 2 ==> 2
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 resolution: (12510) {G1,W13,D3,L3,V3,M3} { ! convergent_lines(
% 103.67/104.03 orthogonal_through_point( X, Y ), Z ), convergent_lines( Z, X ), !
% 103.67/104.03 unorthogonal_lines( orthogonal_through_point( X, Y ), Z ) }.
% 103.67/104.03 parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 103.67/104.03 orthogonal_through_point( Y, X ), Y ) }.
% 103.67/104.03 parent1[2]: (274) {G1,W12,D2,L4,V3,M2} R(18,21) { ! convergent_lines( X, Y
% 103.67/104.03 ), convergent_lines( Y, Z ), unorthogonal_lines( X, Z ), !
% 103.67/104.03 unorthogonal_lines( X, Y ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := Y
% 103.67/104.03 Y := X
% 103.67/104.03 end
% 103.67/104.03 substitution1:
% 103.67/104.03 X := orthogonal_through_point( X, Y )
% 103.67/104.03 Y := Z
% 103.67/104.03 Z := X
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 resolution: (12512) {G2,W11,D3,L3,V3,M3} { convergent_lines( Z, X ), !
% 103.67/104.03 unorthogonal_lines( orthogonal_through_point( X, Y ), Z ),
% 103.67/104.03 convergent_lines( Z, X ) }.
% 103.67/104.03 parent0[0]: (12510) {G1,W13,D3,L3,V3,M3} { ! convergent_lines(
% 103.67/104.03 orthogonal_through_point( X, Y ), Z ), convergent_lines( Z, X ), !
% 103.67/104.03 unorthogonal_lines( orthogonal_through_point( X, Y ), Z ) }.
% 103.67/104.03 parent1[1]: (91) {G3,W8,D3,L2,V3,M2} R(40,43) { convergent_lines( Z, X ),
% 103.67/104.03 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 Z := Z
% 103.67/104.03 end
% 103.67/104.03 substitution1:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 Z := Z
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 factor: (12513) {G2,W8,D3,L2,V3,M2} { convergent_lines( X, Y ), !
% 103.67/104.03 unorthogonal_lines( orthogonal_through_point( Y, Z ), X ) }.
% 103.67/104.03 parent0[0, 2]: (12512) {G2,W11,D3,L3,V3,M3} { convergent_lines( Z, X ), !
% 103.67/104.03 unorthogonal_lines( orthogonal_through_point( X, Y ), Z ),
% 103.67/104.03 convergent_lines( Z, X ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := Y
% 103.67/104.03 Y := Z
% 103.67/104.03 Z := X
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (2961) {G4,W8,D3,L2,V3,M1} R(274,23);r(91) { convergent_lines
% 103.67/104.03 ( Z, X ), ! unorthogonal_lines( orthogonal_through_point( X, Y ), Z ) }.
% 103.67/104.03 parent0: (12513) {G2,W8,D3,L2,V3,M2} { convergent_lines( X, Y ), !
% 103.67/104.03 unorthogonal_lines( orthogonal_through_point( Y, Z ), X ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := Z
% 103.67/104.03 Y := X
% 103.67/104.03 Z := Y
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 0
% 103.67/104.03 1 ==> 1
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 resolution: (12514) {G2,W16,D3,L4,V4,M4} { convergent_lines( X, Y ), !
% 103.67/104.03 convergent_lines( T, orthogonal_through_point( Y, Z ) ), convergent_lines
% 103.67/104.03 ( T, X ), ! unorthogonal_lines( T, orthogonal_through_point( Y, Z ) ) }.
% 103.67/104.03 parent0[1]: (2961) {G4,W8,D3,L2,V3,M1} R(274,23);r(91) { convergent_lines(
% 103.67/104.03 Z, X ), ! unorthogonal_lines( orthogonal_through_point( X, Y ), Z ) }.
% 103.67/104.03 parent1[3]: (289) {G1,W12,D2,L4,V3,M2} R(19,20) { ! convergent_lines( X, Y
% 103.67/104.03 ), convergent_lines( X, Z ), ! unorthogonal_lines( X, Y ),
% 103.67/104.03 unorthogonal_lines( Y, Z ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := Y
% 103.67/104.03 Y := Z
% 103.67/104.03 Z := X
% 103.67/104.03 end
% 103.67/104.03 substitution1:
% 103.67/104.03 X := T
% 103.67/104.03 Y := orthogonal_through_point( Y, Z )
% 103.67/104.03 Z := X
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (2965) {G5,W16,D3,L4,V4,M1} R(2961,289) { convergent_lines( X
% 103.67/104.03 , Y ), ! convergent_lines( Z, orthogonal_through_point( Y, T ) ),
% 103.67/104.03 convergent_lines( Z, X ), ! unorthogonal_lines( Z,
% 103.67/104.03 orthogonal_through_point( Y, T ) ) }.
% 103.67/104.03 parent0: (12514) {G2,W16,D3,L4,V4,M4} { convergent_lines( X, Y ), !
% 103.67/104.03 convergent_lines( T, orthogonal_through_point( Y, Z ) ), convergent_lines
% 103.67/104.03 ( T, X ), ! unorthogonal_lines( T, orthogonal_through_point( Y, Z ) ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 Z := T
% 103.67/104.03 T := Z
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 0
% 103.67/104.03 1 ==> 1
% 103.67/104.03 2 ==> 2
% 103.67/104.03 3 ==> 3
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 factor: (12516) {G5,W13,D3,L3,V2,M3} { convergent_lines( X, X ), !
% 103.67/104.03 convergent_lines( X, orthogonal_through_point( X, Y ) ), !
% 103.67/104.03 unorthogonal_lines( X, orthogonal_through_point( X, Y ) ) }.
% 103.67/104.03 parent0[0, 2]: (2965) {G5,W16,D3,L4,V4,M1} R(2961,289) { convergent_lines(
% 103.67/104.03 X, Y ), ! convergent_lines( Z, orthogonal_through_point( Y, T ) ),
% 103.67/104.03 convergent_lines( Z, X ), ! unorthogonal_lines( Z,
% 103.67/104.03 orthogonal_through_point( Y, T ) ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := X
% 103.67/104.03 Z := X
% 103.67/104.03 T := Y
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 resolution: (12517) {G1,W10,D3,L2,V2,M2} { ! convergent_lines( X,
% 103.67/104.03 orthogonal_through_point( X, Y ) ), ! unorthogonal_lines( X,
% 103.67/104.03 orthogonal_through_point( X, Y ) ) }.
% 103.67/104.03 parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 103.67/104.03 parent1[0]: (12516) {G5,W13,D3,L3,V2,M3} { convergent_lines( X, X ), !
% 103.67/104.03 convergent_lines( X, orthogonal_through_point( X, Y ) ), !
% 103.67/104.03 unorthogonal_lines( X, orthogonal_through_point( X, Y ) ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 end
% 103.67/104.03 substitution1:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (2966) {G6,W10,D3,L2,V2,M1} F(2965);r(2) { ! convergent_lines
% 103.67/104.03 ( X, orthogonal_through_point( X, Y ) ), ! unorthogonal_lines( X,
% 103.67/104.03 orthogonal_through_point( X, Y ) ) }.
% 103.67/104.03 parent0: (12517) {G1,W10,D3,L2,V2,M2} { ! convergent_lines( X,
% 103.67/104.03 orthogonal_through_point( X, Y ) ), ! unorthogonal_lines( X,
% 103.67/104.03 orthogonal_through_point( X, Y ) ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 0
% 103.67/104.03 1 ==> 1
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 resolution: (12518) {G3,W5,D3,L1,V2,M1} { ! unorthogonal_lines( X,
% 103.67/104.03 orthogonal_through_point( X, Y ) ) }.
% 103.67/104.03 parent0[0]: (2966) {G6,W10,D3,L2,V2,M1} F(2965);r(2) { ! convergent_lines(
% 103.67/104.03 X, orthogonal_through_point( X, Y ) ), ! unorthogonal_lines( X,
% 103.67/104.03 orthogonal_through_point( X, Y ) ) }.
% 103.67/104.03 parent1[0]: (46) {G2,W5,D3,L1,V2,M1} R(43,37) { convergent_lines( X,
% 103.67/104.03 orthogonal_through_point( X, Y ) ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 end
% 103.67/104.03 substitution1:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (2967) {G7,W5,D3,L1,V2,M1} S(2966);r(46) { !
% 103.67/104.03 unorthogonal_lines( X, orthogonal_through_point( X, Y ) ) }.
% 103.67/104.03 parent0: (12518) {G3,W5,D3,L1,V2,M1} { ! unorthogonal_lines( X,
% 103.67/104.03 orthogonal_through_point( X, Y ) ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 0
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 resolution: (12522) {G2,W15,D2,L5,V3,M5} { ! convergent_lines( X, Y ),
% 103.67/104.03 distinct_lines( X, Z ), convergent_lines( Y, Z ), ! distinct_lines( Y, Z
% 103.67/104.03 ), ! convergent_lines( X, Y ) }.
% 103.67/104.03 parent0[2]: (2354) {G3,W11,D3,L3,V3,M1} F(2328);r(34) { ! convergent_lines
% 103.67/104.03 ( Y, Z ), distinct_lines( Y, X ), ! apart_point_and_line(
% 103.67/104.03 intersection_point( Y, Z ), X ) }.
% 103.67/104.03 parent1[3]: (245) {G1,W14,D3,L4,V3,M1} R(16,9) { convergent_lines( X, Y ),
% 103.67/104.03 ! distinct_lines( X, Y ), ! convergent_lines( Z, X ),
% 103.67/104.03 apart_point_and_line( intersection_point( Z, X ), Y ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := Z
% 103.67/104.03 Y := X
% 103.67/104.03 Z := Y
% 103.67/104.03 end
% 103.67/104.03 substitution1:
% 103.67/104.03 X := Y
% 103.67/104.03 Y := Z
% 103.67/104.03 Z := X
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 factor: (12523) {G2,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ),
% 103.67/104.03 distinct_lines( X, Z ), convergent_lines( Y, Z ), ! distinct_lines( Y, Z
% 103.67/104.03 ) }.
% 103.67/104.03 parent0[0, 4]: (12522) {G2,W15,D2,L5,V3,M5} { ! convergent_lines( X, Y ),
% 103.67/104.03 distinct_lines( X, Z ), convergent_lines( Y, Z ), ! distinct_lines( Y, Z
% 103.67/104.03 ), ! convergent_lines( X, Y ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 Z := Z
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (4368) {G4,W12,D2,L4,V3,M2} R(245,2354);f { convergent_lines(
% 103.67/104.03 X, Y ), ! convergent_lines( Z, X ), distinct_lines( Z, Y ), !
% 103.67/104.03 distinct_lines( X, Y ) }.
% 103.67/104.03 parent0: (12523) {G2,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ),
% 103.67/104.03 distinct_lines( X, Z ), convergent_lines( Y, Z ), ! distinct_lines( Y, Z
% 103.67/104.03 ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := Z
% 103.67/104.03 Y := X
% 103.67/104.03 Z := Y
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 1
% 103.67/104.03 1 ==> 2
% 103.67/104.03 2 ==> 0
% 103.67/104.03 3 ==> 3
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 resolution: (12524) {G2,W12,D2,L4,V3,M4} { convergent_lines( X, Y ), !
% 103.67/104.03 convergent_lines( Z, X ), distinct_lines( Z, Y ), ! distinct_lines( Y, X
% 103.67/104.03 ) }.
% 103.67/104.03 parent0[3]: (4368) {G4,W12,D2,L4,V3,M2} R(245,2354);f { convergent_lines( X
% 103.67/104.03 , Y ), ! convergent_lines( Z, X ), distinct_lines( Z, Y ), !
% 103.67/104.03 distinct_lines( X, Y ) }.
% 103.67/104.03 parent1[1]: (34) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 103.67/104.03 distinct_lines( X, Y ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 Z := Z
% 103.67/104.03 end
% 103.67/104.03 substitution1:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (4384) {G5,W12,D2,L4,V3,M2} R(4368,34) { convergent_lines( X,
% 103.67/104.03 Y ), ! convergent_lines( Z, X ), ! distinct_lines( Y, X ), distinct_lines
% 103.67/104.03 ( Z, Y ) }.
% 103.67/104.03 parent0: (12524) {G2,W12,D2,L4,V3,M4} { convergent_lines( X, Y ), !
% 103.67/104.03 convergent_lines( Z, X ), distinct_lines( Z, Y ), ! distinct_lines( Y, X
% 103.67/104.03 ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 Z := Z
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 0
% 103.67/104.03 1 ==> 1
% 103.67/104.03 2 ==> 3
% 103.67/104.03 3 ==> 2
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 resolution: (12526) {G2,W12,D2,L4,V3,M4} { distinct_lines( Y, X ),
% 103.67/104.03 convergent_lines( Z, Y ), ! convergent_lines( X, Z ), ! distinct_lines( Y
% 103.67/104.03 , Z ) }.
% 103.67/104.03 parent0[0]: (34) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 103.67/104.03 distinct_lines( X, Y ) }.
% 103.67/104.03 parent1[3]: (4384) {G5,W12,D2,L4,V3,M2} R(4368,34) { convergent_lines( X, Y
% 103.67/104.03 ), ! convergent_lines( Z, X ), ! distinct_lines( Y, X ), distinct_lines
% 103.67/104.03 ( Z, Y ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := Y
% 103.67/104.03 Y := X
% 103.67/104.03 end
% 103.67/104.03 substitution1:
% 103.67/104.03 X := Z
% 103.67/104.03 Y := Y
% 103.67/104.03 Z := X
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (4393) {G6,W12,D2,L4,V3,M2} R(4384,34) { convergent_lines( X,
% 103.67/104.03 Y ), ! convergent_lines( Z, X ), distinct_lines( Y, Z ), ! distinct_lines
% 103.67/104.03 ( Y, X ) }.
% 103.67/104.03 parent0: (12526) {G2,W12,D2,L4,V3,M4} { distinct_lines( Y, X ),
% 103.67/104.03 convergent_lines( Z, Y ), ! convergent_lines( X, Z ), ! distinct_lines( Y
% 103.67/104.03 , Z ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := Z
% 103.67/104.03 Y := Y
% 103.67/104.03 Z := X
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 2
% 103.67/104.03 1 ==> 0
% 103.67/104.03 2 ==> 1
% 103.67/104.03 3 ==> 3
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 resolution: (12527) {G4,W15,D2,L5,V4,M5} { convergent_lines( X, Y ), !
% 103.67/104.03 convergent_lines( Z, X ), distinct_lines( Y, Z ), distinct_lines( Y, T )
% 103.67/104.03 , ! distinct_lines( X, T ) }.
% 103.67/104.03 parent0[3]: (4393) {G6,W12,D2,L4,V3,M2} R(4384,34) { convergent_lines( X, Y
% 103.67/104.03 ), ! convergent_lines( Z, X ), distinct_lines( Y, Z ), ! distinct_lines
% 103.67/104.03 ( Y, X ) }.
% 103.67/104.03 parent1[0]: (217) {G3,W9,D2,L3,V3,M3} R(35,34) { distinct_lines( Z, X ),
% 103.67/104.03 distinct_lines( Z, Y ), ! distinct_lines( X, Y ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 Z := Z
% 103.67/104.03 end
% 103.67/104.03 substitution1:
% 103.67/104.03 X := X
% 103.67/104.03 Y := T
% 103.67/104.03 Z := Y
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (4397) {G7,W15,D2,L5,V4,M3} R(4393,217) { convergent_lines( X
% 103.67/104.03 , Y ), ! convergent_lines( Z, X ), distinct_lines( Y, T ), !
% 103.67/104.03 distinct_lines( X, T ), distinct_lines( Y, Z ) }.
% 103.67/104.03 parent0: (12527) {G4,W15,D2,L5,V4,M5} { convergent_lines( X, Y ), !
% 103.67/104.03 convergent_lines( Z, X ), distinct_lines( Y, Z ), distinct_lines( Y, T )
% 103.67/104.03 , ! distinct_lines( X, T ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 Z := Z
% 103.67/104.03 T := T
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 0
% 103.67/104.03 1 ==> 1
% 103.67/104.03 2 ==> 4
% 103.67/104.03 3 ==> 2
% 103.67/104.03 4 ==> 3
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 factor: (12531) {G7,W12,D2,L4,V3,M4} { convergent_lines( X, Y ), !
% 103.67/104.03 convergent_lines( Z, X ), distinct_lines( Y, Z ), ! distinct_lines( X, Z
% 103.67/104.03 ) }.
% 103.67/104.03 parent0[2, 4]: (4397) {G7,W15,D2,L5,V4,M3} R(4393,217) { convergent_lines(
% 103.67/104.03 X, Y ), ! convergent_lines( Z, X ), distinct_lines( Y, T ), !
% 103.67/104.03 distinct_lines( X, T ), distinct_lines( Y, Z ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 Z := Z
% 103.67/104.03 T := Z
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (4404) {G8,W12,D2,L4,V3,M2} F(4397) { convergent_lines( X, Y )
% 103.67/104.03 , ! convergent_lines( Z, X ), ! distinct_lines( X, Z ), distinct_lines( Y
% 103.67/104.03 , Z ) }.
% 103.67/104.03 parent0: (12531) {G7,W12,D2,L4,V3,M4} { convergent_lines( X, Y ), !
% 103.67/104.03 convergent_lines( Z, X ), distinct_lines( Y, Z ), ! distinct_lines( X, Z
% 103.67/104.03 ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 Z := Z
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 0
% 103.67/104.03 1 ==> 1
% 103.67/104.03 2 ==> 3
% 103.67/104.03 3 ==> 2
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 resolution: (12533) {G3,W15,D2,L5,V4,M5} { convergent_lines( X, Y ), !
% 103.67/104.03 convergent_lines( Z, X ), distinct_lines( Y, Z ), ! convergent_lines( T,
% 103.67/104.03 Z ), convergent_lines( T, X ) }.
% 103.67/104.03 parent0[2]: (4404) {G8,W12,D2,L4,V3,M2} F(4397) { convergent_lines( X, Y )
% 103.67/104.03 , ! convergent_lines( Z, X ), ! distinct_lines( X, Z ), distinct_lines( Y
% 103.67/104.03 , Z ) }.
% 103.67/104.03 parent1[2]: (222) {G2,W9,D2,L3,V3,M1} R(13,34) { ! convergent_lines( X, Y )
% 103.67/104.03 , convergent_lines( X, Z ), distinct_lines( Z, Y ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 Z := Z
% 103.67/104.03 end
% 103.67/104.03 substitution1:
% 103.67/104.03 X := T
% 103.67/104.03 Y := Z
% 103.67/104.03 Z := X
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (4411) {G9,W15,D2,L5,V4,M1} R(4404,222) { convergent_lines( X
% 103.67/104.03 , Y ), ! convergent_lines( Z, X ), ! convergent_lines( T, Z ),
% 103.67/104.03 convergent_lines( T, X ), distinct_lines( Y, Z ) }.
% 103.67/104.03 parent0: (12533) {G3,W15,D2,L5,V4,M5} { convergent_lines( X, Y ), !
% 103.67/104.03 convergent_lines( Z, X ), distinct_lines( Y, Z ), ! convergent_lines( T,
% 103.67/104.03 Z ), convergent_lines( T, X ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 Z := Z
% 103.67/104.03 T := T
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 0
% 103.67/104.03 1 ==> 1
% 103.67/104.03 2 ==> 4
% 103.67/104.03 3 ==> 2
% 103.67/104.03 4 ==> 3
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 factor: (12538) {G9,W12,D2,L4,V2,M4} { convergent_lines( X, X ), !
% 103.67/104.03 convergent_lines( Y, X ), ! convergent_lines( X, Y ), distinct_lines( X,
% 103.67/104.03 Y ) }.
% 103.67/104.03 parent0[0, 3]: (4411) {G9,W15,D2,L5,V4,M1} R(4404,222) { convergent_lines(
% 103.67/104.03 X, Y ), ! convergent_lines( Z, X ), ! convergent_lines( T, Z ),
% 103.67/104.03 convergent_lines( T, X ), distinct_lines( Y, Z ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := X
% 103.67/104.03 Z := Y
% 103.67/104.03 T := X
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 resolution: (12541) {G1,W9,D2,L3,V2,M3} { ! convergent_lines( Y, X ), !
% 103.67/104.03 convergent_lines( X, Y ), distinct_lines( X, Y ) }.
% 103.67/104.03 parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 103.67/104.03 parent1[0]: (12538) {G9,W12,D2,L4,V2,M4} { convergent_lines( X, X ), !
% 103.67/104.03 convergent_lines( Y, X ), ! convergent_lines( X, Y ), distinct_lines( X,
% 103.67/104.03 Y ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 end
% 103.67/104.03 substitution1:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (4420) {G10,W9,D2,L3,V2,M1} F(4411);r(2) { ! convergent_lines
% 103.67/104.03 ( Y, X ), ! convergent_lines( X, Y ), distinct_lines( X, Y ) }.
% 103.67/104.03 parent0: (12541) {G1,W9,D2,L3,V2,M3} { ! convergent_lines( Y, X ), !
% 103.67/104.03 convergent_lines( X, Y ), distinct_lines( X, Y ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 0
% 103.67/104.03 1 ==> 1
% 103.67/104.03 2 ==> 2
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 resolution: (12545) {G2,W9,D2,L3,V2,M3} { ! convergent_lines( Y, X ),
% 103.67/104.03 distinct_lines( Y, X ), ! convergent_lines( Y, X ) }.
% 103.67/104.03 parent0[0]: (4420) {G10,W9,D2,L3,V2,M1} F(4411);r(2) { ! convergent_lines(
% 103.67/104.03 Y, X ), ! convergent_lines( X, Y ), distinct_lines( X, Y ) }.
% 103.67/104.03 parent1[1]: (43) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 103.67/104.03 convergent_lines( X, Y ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := Y
% 103.67/104.03 Y := X
% 103.67/104.03 end
% 103.67/104.03 substitution1:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 factor: (12547) {G2,W6,D2,L2,V2,M2} { ! convergent_lines( X, Y ),
% 103.67/104.03 distinct_lines( X, Y ) }.
% 103.67/104.03 parent0[0, 2]: (12545) {G2,W9,D2,L3,V2,M3} { ! convergent_lines( Y, X ),
% 103.67/104.03 distinct_lines( Y, X ), ! convergent_lines( Y, X ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := Y
% 103.67/104.03 Y := X
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (4441) {G11,W6,D2,L2,V2,M1} S(4420);r(43) { ! convergent_lines
% 103.67/104.03 ( X, Y ), distinct_lines( X, Y ) }.
% 103.67/104.03 parent0: (12547) {G2,W6,D2,L2,V2,M2} { ! convergent_lines( X, Y ),
% 103.67/104.03 distinct_lines( X, Y ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 0
% 103.67/104.03 1 ==> 1
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 resolution: (12549) {G1,W14,D3,L2,V3,M2} { convergent_lines(
% 103.67/104.03 orthogonal_through_point( Y, X ), parallel_through_point( Z, X ) ), !
% 103.67/104.03 distinct_lines( orthogonal_through_point( Y, X ), parallel_through_point
% 103.67/104.03 ( Z, X ) ) }.
% 103.67/104.03 parent0[0]: (24) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 103.67/104.03 orthogonal_through_point( Y, X ) ) }.
% 103.67/104.03 parent1[2]: (254) {G1,W13,D3,L3,V3,M1} R(16,15) { convergent_lines( X,
% 103.67/104.03 parallel_through_point( Y, Z ) ), ! distinct_lines( X,
% 103.67/104.03 parallel_through_point( Y, Z ) ), apart_point_and_line( Z, X ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 end
% 103.67/104.03 substitution1:
% 103.67/104.03 X := orthogonal_through_point( Y, X )
% 103.67/104.03 Y := Z
% 103.67/104.03 Z := X
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (4540) {G2,W14,D3,L2,V3,M1} R(254,24) { convergent_lines(
% 103.67/104.03 orthogonal_through_point( X, Y ), parallel_through_point( Z, Y ) ), !
% 103.67/104.03 distinct_lines( orthogonal_through_point( X, Y ), parallel_through_point
% 103.67/104.03 ( Z, Y ) ) }.
% 103.67/104.03 parent0: (12549) {G1,W14,D3,L2,V3,M2} { convergent_lines(
% 103.67/104.03 orthogonal_through_point( Y, X ), parallel_through_point( Z, X ) ), !
% 103.67/104.03 distinct_lines( orthogonal_through_point( Y, X ), parallel_through_point
% 103.67/104.03 ( Z, X ) ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := Y
% 103.67/104.03 Y := X
% 103.67/104.03 Z := Z
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 0
% 103.67/104.03 1 ==> 1
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 resolution: (12550) {G1,W17,D3,L3,V4,M3} { ! distinct_lines(
% 103.67/104.03 orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ),
% 103.67/104.03 apart_point_and_line( T, orthogonal_through_point( X, Y ) ),
% 103.67/104.03 apart_point_and_line( T, orthogonal_through_point( X, Z ) ) }.
% 103.67/104.03 parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 103.67/104.03 orthogonal_through_point( Y, X ), Y ) }.
% 103.67/104.03 parent1[3]: (302) {G1,W16,D3,L4,V4,M1} R(25,23) { ! distinct_lines( X,
% 103.67/104.03 orthogonal_through_point( Y, Z ) ), apart_point_and_line( T, X ),
% 103.67/104.03 apart_point_and_line( T, orthogonal_through_point( Y, Z ) ),
% 103.67/104.03 unorthogonal_lines( X, Y ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := Y
% 103.67/104.03 Y := X
% 103.67/104.03 end
% 103.67/104.03 substitution1:
% 103.67/104.03 X := orthogonal_through_point( X, Y )
% 103.67/104.03 Y := X
% 103.67/104.03 Z := Z
% 103.67/104.03 T := T
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 subsumption: (4549) {G2,W17,D3,L3,V4,M2} R(302,23) { ! distinct_lines(
% 103.67/104.03 orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ),
% 103.67/104.03 apart_point_and_line( T, orthogonal_through_point( X, Z ) ),
% 103.67/104.03 apart_point_and_line( T, orthogonal_through_point( X, Y ) ) }.
% 103.67/104.03 parent0: (12550) {G1,W17,D3,L3,V4,M3} { ! distinct_lines(
% 103.67/104.03 orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ),
% 103.67/104.03 apart_point_and_line( T, orthogonal_through_point( X, Y ) ),
% 103.67/104.03 apart_point_and_line( T, orthogonal_through_point( X, Z ) ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 Z := Z
% 103.67/104.03 T := T
% 103.67/104.03 end
% 103.67/104.03 permutation0:
% 103.67/104.03 0 ==> 0
% 103.67/104.03 1 ==> 2
% 103.67/104.03 2 ==> 1
% 103.67/104.03 end
% 103.67/104.03
% 103.67/104.03 resolution: (12552) {G2,W17,D4,L3,V4,M3} { ! distinct_lines(
% 103.67/104.03 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ),
% 103.67/104.03 apart_point_and_line( T, orthogonal_through_point(
% 103.67/104.03 orthogonal_through_point( X, Y ), Z ) ), apart_point_and_line( T, X ) }.
% 103.67/104.03 parent0[0]: (2967) {G7,W5,D3,L1,V2,M1} S(2966);r(46) { ! unorthogonal_lines
% 103.67/104.03 ( X, orthogonal_through_point( X, Y ) ) }.
% 103.67/104.03 parent1[3]: (303) {G1,W16,D3,L4,V4,M1} R(25,23) { ! distinct_lines(
% 103.67/104.03 orthogonal_through_point( X, Y ), Z ), apart_point_and_line( T,
% 103.67/104.03 orthogonal_through_point( X, Y ) ), apart_point_and_line( T, Z ),
% 103.67/104.03 unorthogonal_lines( Z, X ) }.
% 103.67/104.03 substitution0:
% 103.67/104.03 X := X
% 103.67/104.03 Y := Y
% 103.67/104.03 end
% 103.67/104.03 substitution1:
% 103.67/104.03 X := orthogonal_through_point( X, Y )
% 103.67/104.03 Y := Z
% 103.67/104.03 Z := X
% 103.67/104.04 T := T
% 103.67/104.04 end
% 103.67/104.04
% 103.67/104.04 subsumption: (4550) {G8,W17,D4,L3,V4,M2} R(303,2967) { ! distinct_lines(
% 103.67/104.04 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ),
% 103.67/104.04 apart_point_and_line( T, X ), apart_point_and_line( T,
% 103.67/104.04 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ) ) }.
% 103.67/104.04 parent0: (12552) {G2,W17,D4,L3,V4,M3} { ! distinct_lines(
% 103.67/104.04 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ),
% 103.67/104.04 apart_point_and_line( T, orthogonal_through_point(
% 103.67/104.04 orthogonal_through_point( X, Y ), Z ) ), apart_point_and_line( T, X ) }.
% 103.67/104.04 substitution0:
% 103.67/104.04 X := X
% 103.67/104.04 Y := Y
% 103.67/104.04 Z := Z
% 103.67/104.04 T := T
% 103.67/104.04 end
% 103.67/104.04 permutation0:
% 103.67/104.04 0 ==> 0
% 103.67/104.04 1 ==> 2
% 103.67/104.04 2 ==> 1
% 103.67/104.04 end
% 103.67/104.04
% 103.67/104.04 resolution: (12553) {G3,W9,D4,L1,V0,M1} { convergent_lines(
% 103.67/104.04 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 103.67/104.04 ), parallel_through_point( skol2, skol1 ) ) }.
% 103.67/104.04 parent0[1]: (4540) {G2,W14,D3,L2,V3,M1} R(254,24) { convergent_lines(
% 103.67/104.04 orthogonal_through_point( X, Y ), parallel_through_point( Z, Y ) ), !
% 103.67/104.04 distinct_lines( orthogonal_through_point( X, Y ), parallel_through_point
% 103.67/104.04 ( Z, Y ) ) }.
% 103.67/104.04 parent1[0]: (300) {G2,W9,D4,L1,V0,M1} R(26,34) { distinct_lines(
% 103.67/104.04 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 103.67/104.04 ), parallel_through_point( skol2, skol1 ) ) }.
% 103.67/104.04 substitution0:
% 103.67/104.04 X := orthogonal_through_point( skol2, skol1 )
% 103.67/104.04 Y := skol1
% 103.67/104.04 Z := skol2
% 103.67/104.04 end
% 103.67/104.04 substitution1:
% 103.67/104.04 end
% 103.67/104.04
% 103.67/104.04 subsumption: (4959) {G3,W9,D4,L1,V0,M1} R(4540,300) { convergent_lines(
% 103.67/104.04 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 103.67/104.04 ), parallel_through_point( skol2, skol1 ) ) }.
% 103.67/104.04 parent0: (12553) {G3,W9,D4,L1,V0,M1} { convergent_lines(
% 103.67/104.04 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 103.67/104.04 ), parallel_through_point( skol2, skol1 ) ) }.
% 103.67/104.04 substitution0:
% 103.67/104.04 end
% 103.67/104.04 permutation0:
% 103.67/104.04 0 ==> 0
% 103.67/104.04 end
% 103.67/104.04
% 103.67/104.04 resolution: (12554) {G3,W10,D4,L2,V1,M2} { convergent_lines(
% 103.67/104.04 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 103.67/104.04 ), X ), convergent_lines( X, skol2 ) }.
% 103.67/104.04 parent0[1]: (125) {G2,W11,D3,L3,V4,M3} R(41,5) { convergent_lines( Z, X ),
% 103.67/104.04 ! convergent_lines( Z, parallel_through_point( Y, T ) ), convergent_lines
% 103.67/104.04 ( X, Y ) }.
% 103.67/104.04 parent1[0]: (4959) {G3,W9,D4,L1,V0,M1} R(4540,300) { convergent_lines(
% 103.67/104.04 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 103.67/104.04 ), parallel_through_point( skol2, skol1 ) ) }.
% 103.67/104.04 substitution0:
% 103.67/104.04 X := X
% 103.67/104.04 Y := skol2
% 103.67/104.04 Z := orthogonal_through_point( orthogonal_through_point( skol2, skol1 )
% 103.67/104.04 , skol1 )
% 103.67/104.04 T := skol1
% 103.67/104.04 end
% 103.67/104.04 substitution1:
% 103.67/104.04 end
% 103.67/104.04
% 103.67/104.04 subsumption: (5045) {G4,W10,D4,L2,V1,M2} R(4959,125) { convergent_lines( X
% 103.67/104.04 , skol2 ), convergent_lines( orthogonal_through_point(
% 103.67/104.04 orthogonal_through_point( skol2, skol1 ), skol1 ), X ) }.
% 103.67/104.04 parent0: (12554) {G3,W10,D4,L2,V1,M2} { convergent_lines(
% 103.67/104.04 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 103.67/104.04 ), X ), convergent_lines( X, skol2 ) }.
% 103.67/104.04 substitution0:
% 103.67/104.04 X := X
% 103.67/104.04 end
% 103.67/104.04 permutation0:
% 103.67/104.04 0 ==> 1
% 103.67/104.04 1 ==> 0
% 103.67/104.04 end
% 103.67/104.04
% 103.67/104.04 resolution: (12556) {G1,W12,D3,L2,V3,M2} { ! distinct_lines(
% 103.67/104.04 orthogonal_through_point( Y, X ), orthogonal_through_point( Y, Z ) ),
% 103.67/104.04 apart_point_and_line( X, orthogonal_through_point( Y, Z ) ) }.
% 103.67/104.04 parent0[0]: (24) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 103.67/104.04 orthogonal_through_point( Y, X ) ) }.
% 103.67/104.04 parent1[2]: (4549) {G2,W17,D3,L3,V4,M2} R(302,23) { ! distinct_lines(
% 103.67/104.04 orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ),
% 103.67/104.04 apart_point_and_line( T, orthogonal_through_point( X, Z ) ),
% 103.67/104.04 apart_point_and_line( T, orthogonal_through_point( X, Y ) ) }.
% 103.67/104.04 substitution0:
% 103.67/104.04 X := X
% 103.67/104.04 Y := Y
% 103.67/104.04 end
% 103.67/104.04 substitution1:
% 103.67/104.04 X := Y
% 103.67/104.04 Y := X
% 103.67/104.04 Z := Z
% 103.67/104.04 T := X
% 103.67/104.04 end
% 103.67/104.04
% 103.67/104.04 subsumption: (6163) {G3,W12,D3,L2,V3,M1} R(4549,24) { ! distinct_lines(
% 103.67/104.04 orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ),
% 103.67/104.04 apart_point_and_line( Y, orthogonal_through_point( X, Z ) ) }.
% 103.67/104.04 parent0: (12556) {G1,W12,D3,L2,V3,M2} { ! distinct_lines(
% 103.67/104.04 orthogonal_through_point( Y, X ), orthogonal_through_point( Y, Z ) ),
% 103.67/104.04 apart_point_and_line( X, orthogonal_through_point( Y, Z ) ) }.
% 103.67/104.04 substitution0:
% 103.67/104.04 X := Y
% 103.67/104.04 Y := X
% 103.67/104.04 Z := Z
% 103.67/104.04 end
% 103.67/104.04 permutation0:
% 103.67/104.04 0 ==> 0
% 103.67/104.04 1 ==> 1
% 103.67/104.04 end
% 103.67/104.04
% 103.67/104.04 resolution: (12558) {G4,W14,D3,L2,V4,M2} { distinct_lines(
% 103.67/104.04 orthogonal_through_point( X, Y ), orthogonal_through_point( Z, T ) ), !
% 103.67/104.04 distinct_lines( orthogonal_through_point( Z, Y ),
% 103.67/104.04 orthogonal_through_point( Z, T ) ) }.
% 103.67/104.04 parent0[1]: (1215) {G4,W8,D3,L2,V3,M1} F(1213);r(34) { distinct_lines(
% 103.67/104.04 orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 103.67/104.04 parent1[1]: (6163) {G3,W12,D3,L2,V3,M1} R(4549,24) { ! distinct_lines(
% 103.67/104.04 orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ),
% 103.67/104.04 apart_point_and_line( Y, orthogonal_through_point( X, Z ) ) }.
% 103.67/104.04 substitution0:
% 103.67/104.04 X := orthogonal_through_point( Z, T )
% 103.67/104.04 Y := X
% 103.67/104.04 Z := Y
% 103.67/104.04 end
% 103.67/104.04 substitution1:
% 103.67/104.04 X := Z
% 103.67/104.04 Y := Y
% 103.67/104.04 Z := T
% 103.67/104.04 end
% 103.67/104.04
% 103.67/104.04 subsumption: (6393) {G5,W14,D3,L2,V4,M2} R(6163,1215) { distinct_lines(
% 103.67/104.04 orthogonal_through_point( T, Y ), orthogonal_through_point( X, Z ) ), !
% 103.67/104.04 distinct_lines( orthogonal_through_point( X, Y ),
% 103.67/104.04 orthogonal_through_point( X, Z ) ) }.
% 103.67/104.04 parent0: (12558) {G4,W14,D3,L2,V4,M2} { distinct_lines(
% 103.67/104.04 orthogonal_through_point( X, Y ), orthogonal_through_point( Z, T ) ), !
% 103.67/104.04 distinct_lines( orthogonal_through_point( Z, Y ),
% 103.67/104.04 orthogonal_through_point( Z, T ) ) }.
% 103.67/104.04 substitution0:
% 103.67/104.04 X := T
% 103.67/104.04 Y := Y
% 103.67/104.04 Z := X
% 103.67/104.04 T := Z
% 103.67/104.04 end
% 103.67/104.04 permutation0:
% 103.67/104.04 0 ==> 0
% 103.67/104.04 1 ==> 1
% 103.67/104.04 end
% 103.67/104.04
% 103.67/104.04 resolution: (12559) {G1,W16,D5,L2,V3,M2} { ! convergent_lines(
% 103.67/104.04 orthogonal_through_point( X, Y ), Z ), ! distinct_lines(
% 103.67/104.04 orthogonal_through_point( X, intersection_point( orthogonal_through_point
% 103.67/104.04 ( X, Y ), Z ) ), orthogonal_through_point( X, Y ) ) }.
% 103.67/104.04 parent0[1]: (8) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), !
% 103.67/104.04 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 103.67/104.04 parent1[1]: (6163) {G3,W12,D3,L2,V3,M1} R(4549,24) { ! distinct_lines(
% 103.67/104.04 orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ),
% 103.67/104.04 apart_point_and_line( Y, orthogonal_through_point( X, Z ) ) }.
% 103.67/104.04 substitution0:
% 103.67/104.04 X := orthogonal_through_point( X, Y )
% 103.67/104.04 Y := Z
% 103.67/104.04 end
% 103.67/104.04 substitution1:
% 103.67/104.04 X := X
% 103.67/104.04 Y := intersection_point( orthogonal_through_point( X, Y ), Z )
% 103.67/104.04 Z := Y
% 103.67/104.04 end
% 103.67/104.04
% 103.67/104.04 subsumption: (6399) {G4,W16,D5,L2,V3,M1} R(6163,8) { ! convergent_lines(
% 103.67/104.04 orthogonal_through_point( X, Y ), Z ), ! distinct_lines(
% 103.67/104.04 orthogonal_through_point( X, intersection_point( orthogonal_through_point
% 103.67/104.04 ( X, Y ), Z ) ), orthogonal_through_point( X, Y ) ) }.
% 103.67/104.04 parent0: (12559) {G1,W16,D5,L2,V3,M2} { ! convergent_lines(
% 103.67/104.04 orthogonal_through_point( X, Y ), Z ), ! distinct_lines(
% 103.67/104.04 orthogonal_through_point( X, intersection_point( orthogonal_through_point
% 103.67/104.04 ( X, Y ), Z ) ), orthogonal_through_point( X, Y ) ) }.
% 103.67/104.04 substitution0:
% 103.67/104.04 X := X
% 103.67/104.04 Y := Y
% 103.67/104.04 Z := Z
% 103.67/104.04 end
% 103.67/104.04 permutation0:
% 103.67/104.04 0 ==> 0
% 103.67/104.04 1 ==> 1
% 103.67/104.04 end
% 103.67/104.04
% 103.67/104.04 resolution: (12560) {G6,W14,D3,L2,V4,M2} { distinct_lines(
% 103.67/104.04 orthogonal_through_point( X, Y ), orthogonal_through_point( Z, T ) ), !
% 103.67/104.04 convergent_lines( orthogonal_through_point( Z, Y ),
% 103.67/104.04 orthogonal_through_point( Z, T ) ) }.
% 103.67/104.04 parent0[1]: (6393) {G5,W14,D3,L2,V4,M2} R(6163,1215) { distinct_lines(
% 103.67/104.04 orthogonal_through_point( T, Y ), orthogonal_through_point( X, Z ) ), !
% 103.67/104.04 distinct_lines( orthogonal_through_point( X, Y ),
% 103.67/104.04 orthogonal_through_point( X, Z ) ) }.
% 103.67/104.04 parent1[1]: (4441) {G11,W6,D2,L2,V2,M1} S(4420);r(43) { ! convergent_lines
% 103.67/104.04 ( X, Y ), distinct_lines( X, Y ) }.
% 103.67/104.04 substitution0:
% 103.67/104.04 X := Z
% 103.67/104.04 Y := Y
% 103.67/104.04 Z := T
% 103.67/104.04 T := X
% 103.67/104.04 end
% 103.67/104.04 substitution1:
% 103.67/104.04 X := orthogonal_through_point( Z, Y )
% 103.67/104.04 Y := orthogonal_through_point( Z, T )
% 103.67/104.04 end
% 103.67/104.04
% 103.67/104.04 subsumption: (6503) {G12,W14,D3,L2,V4,M1} R(6393,4441) { ! convergent_lines
% 103.67/104.04 ( orthogonal_through_point( Z, Y ), orthogonal_through_point( Z, T ) ),
% 103.67/104.04 distinct_lines( orthogonal_through_point( X, Y ),
% 103.67/104.04 orthogonal_through_point( Z, T ) ) }.
% 103.67/104.04 parent0: (12560) {G6,W14,D3,L2,V4,M2} { distinct_lines(
% 103.67/104.04 orthogonal_through_point( X, Y ), orthogonal_through_point( Z, T ) ), !
% 103.67/104.04 convergent_lines( orthogonal_through_point( Z, Y ),
% 103.67/104.04 orthogonal_through_point( Z, T ) ) }.
% 103.67/104.04 substitution0:
% 103.67/104.04 X := X
% 103.67/104.04 Y := Y
% 103.67/104.04 Z := Z
% 103.67/104.04 T := T
% 103.67/104.04 end
% 103.67/104.04 permutation0:
% 103.67/104.04 0 ==> 1
% 103.67/104.04 1 ==> 0
% 103.67/104.04 end
% 103.67/104.04
% 103.67/104.04 resolution: (12561) {G2,W14,D3,L2,V4,M2} { distinct_lines(
% 103.67/104.04 orthogonal_through_point( Z, T ), orthogonal_through_point( X, Y ) ), !
% 103.67/104.04 convergent_lines( orthogonal_through_point( Z, Y ),
% 103.67/104.04 orthogonal_through_point( Z, T ) ) }.
% 103.67/104.04 parent0[0]: (34) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 103.67/104.04 distinct_lines( X, Y ) }.
% 103.67/104.04 parent1[1]: (6503) {G12,W14,D3,L2,V4,M1} R(6393,4441) { ! convergent_lines
% 103.67/104.04 ( orthogonal_through_point( Z, Y ), orthogonal_through_point( Z, T ) ),
% 103.67/104.04 distinct_lines( orthogonal_through_point( X, Y ),
% 103.67/104.04 orthogonal_through_point( Z, T ) ) }.
% 103.67/104.04 substitution0:
% 103.67/104.04 X := orthogonal_through_point( Z, T )
% 103.67/104.04 Y := orthogonal_through_point( X, Y )
% 103.67/104.04 end
% 103.67/104.04 substitution1:
% 103.67/104.04 X := X
% 103.67/104.04 Y := Y
% 103.67/104.04 Z := Z
% 103.67/104.04 T := T
% 103.67/104.04 end
% 103.67/104.04
% 103.67/104.04 subsumption: (6558) {G13,W14,D3,L2,V4,M1} R(6503,34) { ! convergent_lines(
% 103.67/104.04 orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ),
% 103.67/104.04 distinct_lines( orthogonal_through_point( X, Z ),
% 103.67/104.04 orthogonal_through_point( T, Y ) ) }.
% 103.67/104.04 parent0: (12561) {G2,W14,D3,L2,V4,M2} { distinct_lines(
% 103.67/104.04 orthogonal_through_point( Z, T ), orthogonal_through_point( X, Y ) ), !
% 103.67/104.04 convergent_lines( orthogonal_through_point( Z, Y ),
% 103.67/104.04 orthogonal_through_point( Z, T ) ) }.
% 103.67/104.04 substitution0:
% 103.67/104.04 X := T
% 103.67/104.04 Y := Y
% 103.67/104.04 Z := X
% 103.67/104.04 T := Z
% 103.67/104.04 end
% 103.67/104.04 permutation0:
% 103.67/104.04 0 ==> 1
% 103.67/104.04 1 ==> 0
% 103.67/104.04 end
% 103.67/104.04
% 103.67/104.04 resolution: (12562) {G5,W16,D5,L2,V3,M2} { ! convergent_lines(
% 103.67/104.04 orthogonal_through_point( X, Y ), Z ), ! convergent_lines(
% 103.67/104.04 orthogonal_through_point( X, Y ), orthogonal_through_point( X,
% 103.67/104.04 intersection_point( orthogonal_through_point( X, Y ), Z ) ) ) }.
% 103.67/104.04 parent0[1]: (6399) {G4,W16,D5,L2,V3,M1} R(6163,8) { ! convergent_lines(
% 103.67/104.04 orthogonal_through_point( X, Y ), Z ), ! distinct_lines(
% 103.67/104.04 orthogonal_through_point( X, intersection_point( orthogonal_through_point
% 103.67/104.04 ( X, Y ), Z ) ), orthogonal_through_point( X, Y ) ) }.
% 103.67/104.04 parent1[1]: (6558) {G13,W14,D3,L2,V4,M1} R(6503,34) { ! convergent_lines(
% 103.67/104.04 orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ),
% 103.67/104.04 distinct_lines( orthogonal_through_point( X, Z ),
% 103.67/104.04 orthogonal_through_point( T, Y ) ) }.
% 103.67/104.04 substitution0:
% 103.67/104.04 X := X
% 103.67/104.04 Y := Y
% 103.67/104.04 Z := Z
% 103.67/104.04 end
% 103.67/104.04 substitution1:
% 103.67/104.04 X := X
% 103.67/104.04 Y := Y
% 103.67/104.04 Z := intersection_point( orthogonal_through_point( X, Y ), Z )
% 103.67/104.04 T := X
% 103.67/104.04 end
% 103.67/104.04
% 103.67/104.04 subsumption: (7216) {G14,W16,D5,L2,V3,M2} R(6399,6558) { ! convergent_lines
% 103.67/104.04 ( orthogonal_through_point( X, Y ), orthogonal_through_point( X,
% 103.67/104.04 intersection_point( orthogonal_through_point( X, Y ), Z ) ) ), !
% 103.67/104.04 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 103.67/104.04 parent0: (12562) {G5,W16,D5,L2,V3,M2} { ! convergent_lines(
% 103.67/104.04 orthogonal_through_point( X, Y ), Z ), ! convergent_lines(
% 103.67/104.04 orthogonal_through_point( X, Y ), orthogonal_through_point( X,
% 103.67/104.04 intersection_point( orthogonal_through_point( X, Y ), Z ) ) ) }.
% 103.67/104.04 substitution0:
% 103.67/104.04 X := X
% 103.67/104.04 Y := Y
% 103.67/104.04 Z := Z
% 103.67/104.04 end
% 103.67/104.04 permutation0:
% 103.67/104.04 0 ==> 1
% 103.67/104.04 1 ==> 0
% 103.67/104.04 end
% 103.67/104.04
% 103.67/104.04 resolution: (12563) {G5,W16,D5,L2,V3,M2} { ! convergent_lines(
% 103.67/104.04 orthogonal_through_point( X, Y ), Z ), ! convergent_lines(
% 103.67/104.04 orthogonal_through_point( X, intersection_point( orthogonal_through_point
% 103.67/104.04 ( X, Y ), Z ) ), orthogonal_through_point( X, Y ) ) }.
% 103.67/104.04 parent0[1]: (6399) {G4,W16,D5,L2,V3,M1} R(6163,8) { ! convergent_lines(
% 103.67/104.04 orthogonal_through_point( X, Y ), Z ), ! distinct_lines(
% 103.67/104.04 orthogonal_through_point( X, intersection_point( orthogonal_through_point
% 103.67/104.04 ( X, Y ), Z ) ), orthogonal_through_point( X, Y ) ) }.
% 103.67/104.04 parent1[1]: (6503) {G12,W14,D3,L2,V4,M1} R(6393,4441) { ! convergent_lines
% 103.67/104.04 ( orthogonal_through_point( Z, Y ), orthogonal_through_point( Z, T ) ),
% 103.67/104.04 distinct_lines( orthogonal_through_point( X, Y ),
% 103.67/104.04 orthogonal_through_point( Z, T ) ) }.
% 103.67/104.04 substitution0:
% 103.67/104.04 X := X
% 103.67/104.04 Y := Y
% 103.67/104.04 Z := Z
% 103.67/104.04 end
% 103.67/104.04 substitution1:
% 103.67/104.04 X := X
% 103.67/104.04 Y := intersection_point( orthogonal_through_point( X, Y ), Z )
% 103.67/104.04 Z := X
% 103.67/104.04 T := Y
% 103.67/104.04 end
% 103.67/104.04
% 103.67/104.04 subsumption: (7217) {G13,W16,D5,L2,V3,M2} R(6399,6503) { ! convergent_lines
% 103.67/104.04 ( orthogonal_through_point( X, intersection_point(
% 103.67/104.04 orthogonal_through_point( X, Y ), Z ) ), orthogonal_through_point( X, Y )
% 103.67/104.04 ), ! convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 103.67/104.04 parent0: (12563) {G5,W16,D5,L2,V3,M2} { ! convergent_lines(
% 103.67/104.04 orthogonal_through_point( X, Y ), Z ), ! convergent_lines(
% 103.67/104.04 orthogonal_through_point( X, intersection_point( orthogonal_through_point
% 103.67/104.04 ( X, Y ), Z ) ), orthogonal_through_point( X, Y ) ) }.
% 103.67/104.04 substitution0:
% 103.67/104.04 X := X
% 103.67/104.04 Y := Y
% 103.67/104.04 Z := Z
% 103.67/104.04 end
% 103.67/104.04 permutation0:
% 103.67/104.04 0 ==> 1
% 103.67/104.04 1 ==> 0
% 103.67/104.04 end
% 103.67/104.04
% 103.67/104.04 resolution: (12564) {G2,W11,D5,L1,V2,M1} { ! convergent_lines(
% 103.67/104.04 orthogonal_through_point( X, Y ), orthogonal_through_point( X,
% 103.67/104.04 intersection_point( orthogonal_through_point( X, Y ), X ) ) ) }.
% 103.67/104.04 parent0[1]: (7216) {G14,W16,D5,L2,V3,M2} R(6399,6558) { ! convergent_lines
% 103.67/104.04 ( orthogonal_through_point( X, Y ), orthogonal_through_point( X,
% 103.67/104.04 intersection_point( orthogonal_through_point( X, Y ), Z ) ) ), !
% 103.67/104.04 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 103.67/104.04 parent1[0]: (37) {G1,W5,D3,L1,V2,M1} R(17,23) { convergent_lines(
% 103.67/104.04 orthogonal_through_point( X, Y ), X ) }.
% 103.67/104.04 substitution0:
% 103.67/104.04 X := X
% 103.67/104.04 Y := Y
% 103.67/104.04 Z := X
% 103.67/104.04 end
% 103.67/104.04 substitution1:
% 103.67/104.04 X := X
% 103.67/104.04 Y := Y
% 103.67/104.04 end
% 103.67/104.04
% 103.67/104.04 subsumption: (7238) {G15,W11,D5,L1,V2,M1} R(7216,37) { ! convergent_lines(
% 103.67/104.04 orthogonal_through_point( X, Y ), orthogonal_through_point( X,
% 103.67/104.04 intersection_point( orthogonal_through_point( X, Y ), X ) ) ) }.
% 103.67/104.04 parent0: (12564) {G2,W11,D5,L1,V2,M1} { ! convergent_lines(
% 103.67/104.04 orthogonal_through_point( X, Y ), orthogonal_through_point( X,
% 103.67/104.04 intersection_point( orthogonal_through_point( X, Y ), X ) ) ) }.
% 103.67/104.04 substitution0:
% 103.67/104.04 X := X
% 103.67/104.04 Y := Y
% 103.67/104.04 end
% 103.67/104.04 permutation0:
% 103.67/104.04 0 ==> 0
% 103.67/104.04 end
% 103.67/104.04
% 103.67/104.04 resolution: (12565) {G5,W15,D6,L1,V0,M1} { convergent_lines(
% 103.67/104.04 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ),
% 103.67/104.04 intersection_point( orthogonal_through_point( orthogonal_through_point(
% 103.67/104.04 skol2, skol1 ), skol1 ), orthogonal_through_point( skol2, skol1 ) ) ),
% 103.67/104.04 skol2 ) }.
% 103.67/104.04 parent0[0]: (7238) {G15,W11,D5,L1,V2,M1} R(7216,37) { ! convergent_lines(
% 103.67/104.04 orthogonal_through_point( X, Y ), orthogonal_through_point( X,
% 103.67/104.04 intersection_point( orthogonal_through_point( X, Y ), X ) ) ) }.
% 103.67/104.04 parent1[1]: (5045) {G4,W10,D4,L2,V1,M2} R(4959,125) { convergent_lines( X,
% 103.67/104.04 skol2 ), convergent_lines( orthogonal_through_point(
% 103.67/104.04 orthogonal_through_point( skol2, skol1 ), skol1 ), X ) }.
% 103.67/104.04 substitution0:
% 103.67/104.04 X := orthogonal_through_point( skol2, skol1 )
% 103.67/104.04 Y := skol1
% 103.67/104.04 end
% 103.67/104.04 substitution1:
% 103.67/104.04 X := orthogonal_through_point( orthogonal_through_point( skol2, skol1 )
% 103.67/104.04 , intersection_point( orthogonal_through_point( orthogonal_through_point
% 103.67/104.04 ( skol2, skol1 ), skol1 ), orthogonal_through_point( skol2, skol1 ) ) )
% 103.67/104.04 end
% 103.67/104.04
% 103.67/104.04 subsumption: (7269) {G16,W15,D6,L1,V0,M1} R(7238,5045) { convergent_lines(
% 103.67/104.04 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ),
% 103.67/104.04 intersection_point( orthogonal_through_point( orthogonal_through_point(
% 103.67/104.04 skol2, skol1 ), skol1 ), orthogonal_through_point( skol2, skol1 ) ) ),
% 103.67/104.04 skol2 ) }.
% 103.67/104.04 parent0: (12565) {G5,W15,D6,L1,V0,M1} { convergent_lines(
% 103.67/104.04 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ),
% 103.67/104.04 intersection_point( orthogonal_through_point( orthogonal_through_point(
% 103.67/104.04 skol2, skol1 ), skol1 ), orthogonal_through_point( skol2, skol1 ) ) ),
% 103.67/104.04 skol2 ) }.
% 103.67/104.04 substitution0:
% 103.67/104.04 end
% 103.67/104.04 permutation0:
% 103.67/104.04 0 ==> 0
% 103.67/104.04 end
% 103.67/104.04
% 103.67/104.04 resolution: (12567) {G1,W10,D4,L2,V3,M2} { ! distinct_lines(
% 103.67/104.04 orthogonal_through_point( orthogonal_through_point( Y, Z ), X ), Y ),
% 103.67/104.04 apart_point_and_line( X, Y ) }.
% 103.67/104.04 parent0[0]: (24) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 103.67/104.04 orthogonal_through_point( Y, X ) ) }.
% 103.67/104.04 parent1[2]: (4550) {G8,W17,D4,L3,V4,M2} R(303,2967) { ! distinct_lines(
% 103.67/104.04 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ),
% 103.67/104.04 apart_point_and_line( T, X ), apart_point_and_line( T,
% 103.67/104.04 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ) ) }.
% 103.67/104.04 substitution0:
% 103.67/104.04 X := X
% 103.67/104.04 Y := orthogonal_through_point( Y, Z )
% 103.67/104.04 end
% 103.67/104.04 substitution1:
% 103.67/104.04 X := Y
% 103.67/104.04 Y := Z
% 103.67/104.04 Z := X
% 103.67/104.04 T := X
% 103.67/104.04 end
% 103.67/104.04
% 103.67/104.04 subsumption: (7879) {G9,W10,D4,L2,V3,M1} R(4550,24) { ! distinct_lines(
% 103.67/104.04 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ),
% 103.67/104.04 apart_point_and_line( Z, X ) }.
% 103.67/104.04 parent0: (12567) {G1,W10,D4,L2,V3,M2} { ! distinct_lines(
% 103.67/104.04 orthogonal_through_point( orthogonal_through_point( Y, Z ), X ), Y ),
% 103.67/104.04 apart_point_and_line( X, Y ) }.
% 103.67/104.04 substitution0:
% 103.67/104.04 X := Z
% 103.67/104.04 Y := X
% 103.67/104.04 Z := Y
% 103.67/104.04 end
% 103.67/104.04 permutation0:
% 103.67/104.04 0 ==> 0
% 103.67/104.04 1 ==> 1
% 103.67/104.04 end
% 103.67/104.04
% 103.67/104.04 resolution: (12569) {G5,W12,D4,L2,V4,M2} { distinct_lines(
% 103.67/104.04 orthogonal_through_point( X, Y ), Z ), ! distinct_lines(
% 103.67/104.04 orthogonal_through_point( orthogonal_through_point( Z, T ), Y ), Z ) }.
% 103.67/104.04 parent0[1]: (1215) {G4,W8,D3,L2,V3,M1} F(1213);r(34) { distinct_lines(
% 103.67/104.04 orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 103.67/104.04 parent1[1]: (7879) {G9,W10,D4,L2,V3,M1} R(4550,24) { ! distinct_lines(
% 103.67/104.04 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ),
% 103.67/104.04 apart_point_and_line( Z, X ) }.
% 103.67/104.04 substitution0:
% 103.67/104.04 X := Z
% 103.67/104.04 Y := X
% 103.67/104.04 Z := Y
% 103.67/104.04 end
% 103.67/104.04 substitution1:
% 103.67/104.04 X := Z
% 103.67/104.04 Y := T
% 103.67/104.04 Z := Y
% 103.67/104.04 end
% 103.67/104.04
% 103.67/104.04 subsumption: (7931) {G10,W12,D4,L2,V4,M2} R(7879,1215) { distinct_lines(
% 103.67/104.04 orthogonal_through_point( T, Z ), X ), ! distinct_lines(
% 103.67/104.04 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ) }.
% 103.67/104.04 parent0: (12569) {G5,W12,D4,L2,V4,M2} { distinct_lines(
% 103.67/104.04 orthogonal_through_point( X, Y ), Z ), ! distinct_lines(
% 103.67/104.04 orthogonal_through_point( orthogonal_through_point( Z, T ), Y ), Z ) }.
% 103.67/104.04 substitution0:
% 103.67/104.04 X := T
% 103.67/104.04 Y := Z
% 103.67/104.04 Z := X
% 103.67/104.04 T := Y
% 103.67/104.04 end
% 103.67/104.04 permutation0:
% 103.67/104.04 0 ==> 0
% 103.67/104.04 1 ==> 1
% 103.67/104.04 end
% 103.67/104.04
% 103.67/104.04 resolution: (12570) {G1,W12,D4,L2,V3,M2} { ! convergent_lines( X, Y ), !
% 103.67/104.04 distinct_lines( orthogonal_through_point( orthogonal_through_point( Y, Z
% 103.67/104.04 ), intersection_point( X, Y ) ), Y ) }.
% 103.67/104.04 parent0[1]: (9) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), !
% 103.67/104.04 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 103.67/104.04 parent1[1]: (7879) {G9,W10,D4,L2,V3,M1} R(4550,24) { ! distinct_lines(
% 103.67/104.04 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ),
% 103.67/104.04 apart_point_and_line( Z, X ) }.
% 103.67/104.04 substitution0:
% 103.67/104.04 X := X
% 103.67/104.04 Y := Y
% 103.67/104.04 end
% 103.67/104.04 substitution1:
% 103.67/104.04 X := Y
% 103.67/104.04 Y := Z
% 103.67/104.04 Z := intersection_point( X, Y )
% 103.67/104.04 end
% 103.67/104.04
% 103.67/104.04 subsumption: (7938) {G10,W12,D4,L2,V3,M1} R(7879,9) { ! convergent_lines( Z
% 103.67/104.04 , X ), ! distinct_lines( orthogonal_through_point(
% 103.67/104.04 orthogonal_through_point( X, Y ), intersection_point( Z, X ) ), X ) }.
% 103.67/104.04 parent0: (12570) {G1,W12,D4,L2,V3,M2} { ! convergent_lines( X, Y ), !
% 103.67/104.04 distinct_lines( orthogonal_through_point( orthogonal_through_point( Y, Z
% 103.67/104.04 ), intersection_point( X, Y ) ), Y ) }.
% 103.67/104.04 substitution0:
% 103.67/104.04 X := Z
% 103.67/104.04 Y := X
% 103.67/104.04 Z := Y
% 103.67/104.04 end
% 103.67/104.04 permutation0:
% 103.67/104.04 0 ==> 0
% 103.67/104.04 1 ==> 1
% 103.67/104.04 end
% 103.67/104.04
% 103.67/104.04 resolution: (12571) {G11,W12,D4,L2,V4,M2} { distinct_lines(
% 103.67/104.04 orthogonal_through_point( X, Y ), Z ), ! convergent_lines(
% 103.67/104.04 orthogonal_through_point( orthogonal_through_point( Z, T ), Y ), Z ) }.
% 103.67/104.04 parent0[1]: (7931) {G10,W12,D4,L2,V4,M2} R(7879,1215) { distinct_lines(
% 103.67/104.04 orthogonal_through_point( T, Z ), X ), ! distinct_lines(
% 103.67/104.04 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ) }.
% 103.67/104.04 parent1[1]: (4441) {G11,W6,D2,L2,V2,M1} S(4420);r(43) { ! convergent_lines
% 103.67/104.04 ( X, Y ), distinct_lines( X, Y ) }.
% 103.67/104.04 substitution0:
% 103.67/104.04 X := Z
% 103.67/104.04 Y := T
% 103.67/104.04 Z := Y
% 103.67/104.04 T := X
% 103.67/104.04 end
% 103.67/104.04 substitution1:
% 103.67/104.04 X := orthogonal_through_point( orthogonal_through_point( Z, T ), Y )
% 103.67/104.04 Y := Z
% 103.67/104.04 end
% 103.67/104.04
% 103.67/104.04 subsumption: (9772) {G12,W12,D4,L2,V4,M1} R(7931,4441) { ! convergent_lines
% 103.67/104.04 ( orthogonal_through_point( orthogonal_through_point( Z, T ), Y ), Z ),
% 103.67/104.04 distinct_lines( orthogonal_through_point( X, Y ), Z ) }.
% 103.67/104.04 parent0: (12571) {G11,W12,D4,L2,V4,M2} { distinct_lines(
% 103.67/104.04 orthogonal_through_point( X, Y ), Z ), ! convergent_lines(
% 103.67/104.04 orthogonal_through_point( orthogonal_through_point( Z, T ), Y ), Z ) }.
% 103.67/104.04 substitution0:
% 103.67/104.04 X := X
% 103.67/104.04 Y := Y
% 103.67/104.04 Z := Z
% 103.67/104.04 T := T
% 103.67/104.04 end
% 103.67/104.04 permutation0:
% 103.67/104.04 0 ==> 1
% 103.67/104.04 1 ==> 0
% 103.67/104.04 end
% 103.67/104.04
% 103.67/104.04 resolution: (12572) {G11,W12,D4,L2,V3,M2} { ! convergent_lines( X, Y ), !
% 103.67/104.04 convergent_lines( orthogonal_through_point( orthogonal_through_point( Y,
% 103.67/104.04 T ), intersection_point( X, Y ) ), Y ) }.
% 103.67/104.04 parent0[1]: (7938) {G10,W12,D4,L2,V3,M1} R(7879,9) { ! convergent_lines( Z
% 103.67/104.04 , X ), ! distinct_lines( orthogonal_through_point(
% 103.67/104.04 orthogonal_through_point( X, Y ), intersection_point( Z, X ) ), X ) }.
% 103.67/104.04 parent1[1]: (9772) {G12,W12,D4,L2,V4,M1} R(7931,4441) { ! convergent_lines
% 103.67/104.04 ( orthogonal_through_point( orthogonal_through_point( Z, T ), Y ), Z ),
% 103.67/104.04 distinct_lines( orthogonal_through_point( X, Y ), Z ) }.
% 103.67/104.04 substitution0:
% 103.67/104.04 X := Y
% 103.67/104.04 Y := Z
% 103.67/104.04 Z := X
% 103.67/104.04 end
% 103.67/104.04 substitution1:
% 103.67/104.04 X := orthogonal_through_point( Y, Z )
% 103.67/104.04 Y := intersection_point( X, Y )
% 103.67/104.04 Z := Y
% 103.67/104.04 T := T
% 103.67/104.04 end
% 103.67/104.04
% 103.67/104.04 subsumption: (11439) {G13,W12,D4,L2,V3,M2} R(7938,9772) { !
% 103.67/104.04 convergent_lines( orthogonal_through_point( orthogonal_through_point( Y,
% 103.67/104.04 Z ), intersection_point( X, Y ) ), Y ), ! convergent_lines( X, Y ) }.
% 103.67/104.04 parent0: (12572) {G11,W12,D4,L2,V3,M2} { ! convergent_lines( X, Y ), !
% 103.67/104.04 convergent_lines( orthogonal_through_point( orthogonal_through_point( Y,
% 103.67/104.04 T ), intersection_point( X, Y ) ), Y ) }.
% 103.67/104.04 substitution0:
% 103.67/104.04 X := X
% 103.67/104.04 Y := Y
% 103.67/104.04 Z := T
% 103.67/104.04 T := Z
% 103.67/104.04 end
% 103.67/104.04 permutation0:
% 103.67/104.04 0 ==> 1
% 103.67/104.04 1 ==> 0
% 103.67/104.04 end
% 103.67/104.04
% 103.67/104.04 resolution: (12574) {G2,W12,D4,L2,V3,M2} { ! convergent_lines(
% 103.67/104.04 orthogonal_through_point( orthogonal_through_point( X, Y ),
% 103.67/104.04 intersection_point( Z, X ) ), X ), ! convergent_lines( X, Z ) }.
% 103.67/104.04 parent0[1]: (11439) {G13,W12,D4,L2,V3,M2} R(7938,9772) { ! convergent_lines
% 103.67/104.04 ( orthogonal_through_point( orthogonal_through_point( Y, Z ),
% 103.67/104.04 intersection_point( X, Y ) ), Y ), ! convergent_lines( X, Y ) }.
% 103.67/104.04 parent1[1]: (43) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 103.67/104.04 convergent_lines( X, Y ) }.
% 103.67/104.04 substitution0:
% 103.67/104.04 X := Z
% 103.67/104.04 Y := X
% 103.67/104.04 Z := Y
% 103.67/104.04 end
% 103.67/104.04 substitution1:
% 103.67/104.04 X := Z
% 103.67/104.04 Y := X
% 103.67/104.04 end
% 103.67/104.04
% 103.67/104.04 subsumption: (11787) {G14,W12,D4,L2,V3,M2} R(11439,43) { ! convergent_lines
% 103.67/104.04 ( X, Z ), ! convergent_lines( orthogonal_through_point(
% 103.67/104.04 orthogonal_through_point( X, Y ), intersection_point( Z, X ) ), X ) }.
% 103.67/104.04 parent0: (12574) {G2,W12,D4,L2,V3,M2} { ! convergent_lines(
% 103.67/104.04 orthogonal_through_point( orthogonal_through_point( X, Y ),
% 103.67/104.04 intersection_point( Z, X ) ), X ), ! convergent_lines( X, Z ) }.
% 103.67/104.04 substitution0:
% 103.67/104.04 X := X
% 103.67/104.04 Y := Y
% 103.67/104.04 Z := Z
% 103.67/104.04 end
% 103.67/104.04 permutation0:
% 103.67/104.04 0 ==> 1
% 103.67/104.04 1 ==> 0
% 103.67/104.04 end
% 103.67/104.04
% 103.67/104.04 resolution: (12577) {G4,W15,D4,L3,V4,M3} { ! convergent_lines( X, Y ),
% 103.67/104.04 convergent_lines( orthogonal_through_point( orthogonal_through_point( X,
% 103.67/104.04 Z ), intersection_point( Y, X ) ), T ), ! convergent_lines( X, T ) }.
% 103.67/104.04 parent0[1]: (11787) {G14,W12,D4,L2,V3,M2} R(11439,43) { ! convergent_lines
% 103.67/104.04 ( X, Z ), ! convergent_lines( orthogonal_through_point(
% 103.67/104.04 orthogonal_through_point( X, Y ), intersection_point( Z, X ) ), X ) }.
% 103.67/104.04 parent1[0]: (192) {G3,W9,D2,L3,V3,M3} R(44,43) { convergent_lines( Z, X ),
% 103.67/104.04 convergent_lines( Z, Y ), ! convergent_lines( X, Y ) }.
% 103.67/104.04 substitution0:
% 103.67/104.04 X := X
% 103.67/104.04 Y := Z
% 103.67/104.04 Z := Y
% 103.67/104.04 end
% 103.67/104.04 substitution1:
% 103.67/104.04 X := X
% 103.67/104.04 Y := T
% 103.67/104.04 Z := orthogonal_through_point( orthogonal_through_point( X, Z ),
% 103.67/104.04 intersection_point( Y, X ) )
% 103.67/104.04 end
% 103.67/104.04
% 103.67/104.04 subsumption: (12018) {G15,W15,D4,L3,V4,M3} R(11787,192) { convergent_lines
% 103.67/104.04 ( orthogonal_through_point( orthogonal_through_point( X, Z ),
% 103.67/104.04 intersection_point( Y, X ) ), T ), ! convergent_lines( X, T ), !
% 103.67/104.04 convergent_lines( X, Y ) }.
% 103.67/104.04 parent0: (12577) {G4,W15,D4,L3,V4,M3} { ! convergent_lines( X, Y ),
% 103.67/104.04 convergent_lines( orthogonal_through_point( orthogonal_through_point( X,
% 103.67/104.04 Z ), intersection_point( Y, X ) ), T ), ! convergent_lines( X, T ) }.
% 103.67/104.04 substitution0:
% 103.67/104.04 X := X
% 103.67/104.04 Y := Y
% 103.67/104.04 Z := Z
% 103.67/104.04 T := T
% 103.67/104.04 end
% 103.67/104.04 permutation0:
% 103.67/104.04 0 ==> 2
% 103.67/104.04 1 ==> 0
% 103.67/104.04 2 ==> 1
% 103.67/104.04 end
% 103.67/104.04
% 103.67/104.04 factor: (12581) {G15,W12,D4,L2,V3,M2} { convergent_lines(
% 103.67/104.04 orthogonal_through_point( orthogonal_through_point( X, Y ),
% 103.67/104.04 intersection_point( Z, X ) ), Z ), ! convergent_lines( X, Z ) }.
% 103.67/104.04 parent0[1, 2]: (12018) {G15,W15,D4,L3,V4,M3} R(11787,192) {
% 103.67/104.04 convergent_lines( orthogonal_through_point( orthogonal_through_point( X,
% 103.67/104.04 Z ), intersection_point( Y, X ) ), T ), ! convergent_lines( X, T ), !
% 103.67/104.04 convergent_lines( X, Y ) }.
% 103.67/104.04 substitution0:
% 103.67/104.04 X := X
% 103.67/104.04 Y := Z
% 103.67/104.04 Z := Y
% 103.67/104.04 T := Z
% 103.67/104.04 end
% 103.67/104.04
% 103.67/104.04 subsumption: (12034) {G16,W12,D4,L2,V3,M2} F(12018) { ! convergent_lines( X
% 103.67/104.04 , Z ), convergent_lines( orthogonal_through_point(
% 103.67/104.04 orthogonal_through_point( X, Y ), intersection_point( Z, X ) ), Z ) }.
% 103.67/104.04 parent0: (12581) {G15,W12,D4,L2,V3,M2} { convergent_lines(
% 103.67/104.04 orthogonal_through_point( orthogonal_through_point( X, Y ),
% 103.67/104.04 intersection_point( Z, X ) ), Z ), ! convergent_lines( X, Z ) }.
% 103.67/104.04 substitution0:
% 103.67/104.04 X := X
% 103.67/104.04 Y := Y
% 103.67/104.04 Z := Z
% 103.67/104.04 end
% 103.67/104.04 permutation0:
% 103.67/104.04 0 ==> 1
% 103.67/104.04 1 ==> 0
% 103.67/104.04 end
% 103.67/104.04
% 103.67/104.04 resolution: (12582) {G14,W14,D4,L2,V3,M2} { ! convergent_lines(
% 103.67/104.04 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ), !
% 103.67/104.04 convergent_lines( X, orthogonal_through_point( orthogonal_through_point(
% 103.67/104.04 X, Y ), Z ) ) }.
% 103.67/104.04 parent0[0]: (7217) {G13,W16,D5,L2,V3,M2} R(6399,6503) { ! convergent_lines
% 103.67/104.04 ( orthogonal_through_point( X, intersection_point(
% 103.67/104.04 orthogonal_through_point( X, Y ), Z ) ), orthogonal_through_point( X, Y )
% 103.67/104.04 ), ! convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 103.67/104.04 parent1[1]: (12034) {G16,W12,D4,L2,V3,M2} F(12018) { ! convergent_lines( X
% 103.67/104.04 , Z ), convergent_lines( orthogonal_through_point(
% 103.67/104.04 orthogonal_through_point( X, Y ), intersection_point( Z, X ) ), Z ) }.
% 103.67/104.04 substitution0:
% 103.67/104.04 X := orthogonal_through_point( X, Y )
% 103.67/104.04 Y := Z
% 103.67/104.04 Z := X
% 103.67/104.04 end
% 103.67/104.04 substitution1:
% 103.67/104.04 X := X
% 103.67/104.04 Y := Y
% 103.67/104.04 Z := orthogonal_through_point( orthogonal_through_point( X, Y ), Z )
% 103.67/104.04 end
% 103.67/104.04
% 103.67/104.04 resolution: (12585) {G2,W14,D4,L2,V3,M2} { ! convergent_lines(
% 103.67/104.04 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ), !
% 103.67/104.04 convergent_lines( orthogonal_through_point( orthogonal_through_point( X,
% 103.67/104.04 Y ), Z ), X ) }.
% 103.67/104.04 parent0[1]: (12582) {G14,W14,D4,L2,V3,M2} { ! convergent_lines(
% 103.67/104.04 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ), !
% 103.67/104.04 convergent_lines( X, orthogonal_through_point( orthogonal_through_point(
% 103.67/104.04 X, Y ), Z ) ) }.
% 103.67/104.04 parent1[1]: (43) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 103.67/104.04 convergent_lines( X, Y ) }.
% 103.67/104.04 substitution0:
% 103.67/104.04 X := X
% 103.67/104.04 Y := Y
% 103.67/104.04 Z := Z
% 103.67/104.04 end
% 103.67/104.04 substitution1:
% 103.67/104.04 X := X
% 103.67/104.04 Y := orthogonal_through_point( orthogonal_through_point( X, Y ), Z )
% 103.67/104.04 end
% 103.67/104.04
% 103.67/104.04 factor: (12587) {G2,W7,D4,L1,V3,M1} { ! convergent_lines(
% 103.67/104.04 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ) }.
% 103.67/104.04 parent0[0, 1]: (12585) {G2,W14,D4,L2,V3,M2} { ! convergent_lines(
% 103.67/104.04 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ), !
% 103.67/104.04 convergent_lines( orthogonal_through_point( orthogonal_through_point( X,
% 103.67/104.04 Y ), Z ), X ) }.
% 103.67/104.04 substitution0:
% 103.67/104.04 X := X
% 103.67/104.04 Y := Y
% 103.67/104.04 Z := Z
% 103.67/104.04 end
% 103.67/104.04
% 103.67/104.04 subsumption: (12041) {G17,W7,D4,L1,V3,M1} R(12034,7217);r(43) { !
% 103.67/104.04 convergent_lines( orthogonal_through_point( orthogonal_through_point( X,
% 103.67/104.04 Y ), Z ), X ) }.
% 103.67/104.04 parent0: (12587) {G2,W7,D4,L1,V3,M1} { ! convergent_lines(
% 103.67/104.04 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ) }.
% 103.67/104.04 substitution0:
% 103.67/104.04 X := X
% 103.67/104.04 Y := Y
% 103.67/104.04 Z := Z
% 103.67/104.04 end
% 103.67/104.04 permutation0:
% 103.67/104.04 0 ==> 0
% 103.67/104.04 end
% 103.67/104.04
% 103.67/104.04 resolution: (12588) {G17,W0,D0,L0,V0,M0} { }.
% 103.67/104.04 parent0[0]: (12041) {G17,W7,D4,L1,V3,M1} R(12034,7217);r(43) { !
% 103.67/104.04 convergent_lines( orthogonal_through_point( orthogonal_through_point( X,
% 103.67/104.04 Y ), Z ), X ) }.
% 103.67/104.04 parent1[0]: (7269) {G16,W15,D6,L1,V0,M1} R(7238,5045) { convergent_lines(
% 103.67/104.04 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ),
% 103.67/104.04 intersection_point( orthogonal_through_point( orthogonal_through_point(
% 103.67/104.04 skol2, skol1 ), skol1 ), orthogonal_through_point( skol2, skol1 ) ) ),
% 103.67/104.04 skol2 ) }.
% 103.67/104.04 substitution0:
% 103.67/104.04 X := skol2
% 103.67/104.04 Y := skol1
% 103.67/104.04 Z := intersection_point( orthogonal_through_point(
% 103.67/104.04 orthogonal_through_point( skol2, skol1 ), skol1 ),
% 103.67/104.04 orthogonal_through_point( skol2, skol1 ) )
% 103.67/104.04 end
% 103.67/104.04 substitution1:
% 103.67/104.04 end
% 103.67/104.04
% 103.67/104.04 subsumption: (12241) {G18,W0,D0,L0,V0,M0} R(12041,7269) { }.
% 103.67/104.04 parent0: (12588) {G17,W0,D0,L0,V0,M0} { }.
% 103.67/104.04 substitution0:
% 103.67/104.04 end
% 103.67/104.04 permutation0:
% 103.67/104.04 end
% 103.67/104.04
% 103.67/104.04 Proof check complete!
% 103.67/104.04
% 103.67/104.04 Memory use:
% 103.67/104.04
% 103.67/104.04 space for terms: 202939
% 103.67/104.04 space for clauses: 538797
% 103.67/104.04
% 103.67/104.04
% 103.67/104.04 clauses generated: 15581595
% 103.67/104.04 clauses kept: 12242
% 103.67/104.04 clauses selected: 7026
% 103.67/104.04 clauses deleted: 396
% 103.67/104.04 clauses inuse deleted: 28
% 103.67/104.04
% 103.67/104.04 subsentry: 75888115
% 103.67/104.04 literals s-matched: 22665074
% 103.67/104.04 literals matched: 22660634
% 103.67/104.04 full subsumption: 14857467
% 103.67/104.04
% 103.67/104.04 checksum: -1554193961
% 103.67/104.04
% 103.67/104.04
% 103.67/104.04 Bliksem ended
%------------------------------------------------------------------------------